I see this bandied about fairly often on GAF but I really loved my time with this game and I don't remember the game in immense detail but I felt pretty sure I did most battles and that there was a point to them.
So, I did some perusing online on the subject and am going to present some point-counterpoint arguments below, and then please share your thoughts on the matter. Thank you.
Bottom line seems to be: if you want to 100% the game, battles are crucial. If you want to beat the game, battles aren't as important but the more you avoid, the harder the game will be as you go on in the game.
Argument: Battles have a point in Sticker Star
For:
It's the coins they are used for pretty much everything.
If you don't want a lot of back tracking and want to be able to use "thing" stickers freely you'll be dropping lots of coins at the "thing" shop.
It's going to take around 3000 coins to unlock ever secret door.
Boss battles where you use the battle spinner for multiple times will quickly cost a few hundred coins because of the steep price rise every time you use it, and won't reset tillthe end of that battle.
In general there are a number of rarer harder to find stickers that its simply faster to buy than try to find them, pluck it, completely leave the area, and then come back in. In addition there are still plenty of stickers you only get in shops which are nice to have. Shops increase their inventories throughout the game and become actually a very good place to quickly restock on stickers.
Also While it's merely an achievement there is a flag that require you to spend 10,000 coins in shops with the Thing Shop not counting as a a shop.
Basically when you have a surplus of coins you're completely free, you can move as you please as there are little restrictions. When you start to run low on coins that's when the game becomes more confining, requires more backtracking, and in general becomes more tedious.
So the point of battles is for coins, battles themselves don't give that many coins it's the coin bonus your after. When you grab a sticker comet piece at the end of a level you get a coin bonus based on how many enemies you killed. Kill a few enemies or none and get like 3 coins, kill most of the enemies can easily net you 200 or more coins the coin bonuses become quite hefty later on.
Ultimately though there really isn't a good reason to avoid battles. You don't need to worry about wasting stickers. They give you an overabundance of stickers all over fields, and stickers and blocks restock upon leaving and re-entering a level. In addition as long as you have coins you can easily replace most any sticker just by stopping at some of the shops. Don't worry about wasting a rare sticker either as you'll either be able to buy it later, it will respawn, or you'll find more of them. Sure i mean you won't wanna go wasting your best stickers on small fries but the cheaper things you can stock up on quickly make your life easier.
The only time battles are honestly pointless is in a royal sticker crown boss level. This is because those levels don't have sticker comet pieces so you get no coin bonus. Meaning enemies in boss levels actually are a waste of time for the most part unless you can kill them fast then they are still a great money source.
http://www.gamefaqs.com/boards/997828-paper-mario-sticker-star/64862206
Combat isn't pointless if you're going for 100% completion. You need a lot of money in this game if you want to buy all the doors you need for the secrets and combat is the best way to get it. There's also the flags in Decalburg and certain stickers that you can only get from enemies if you want to complete the museum.
http://www.gamefaqs.com/boards/997828-paper-mario-sticker-star/68337937
Against:
The 'interesting' combat system was not interesting because it taught me to avoid combat. I don't call potholes in the road interesting, I just drive around them and recognize them as a nuisance.
Combat wasted stickers and then gave you fewer stickers than you used. Net loss there. It'd waste Coins on the roulette trying to finish things up without being beat up too badly, then give you half a dozen Coins. Net loss there. So, you finished a battle, you now have FEWER stickers, LESS health, FEWER coins, LESS time in the day.
So now I'm avoiding battle, a few segregated stages in. Awesome. So now, with all my stickers I'm pulling off the landscape, I hit the page limit. FUCK the page limit. Why are you limiting my stickers? It's completely arbitrary. Maybe if I had more than a couple dozen, I would be more willing to jump into battle to burn a few. But as it stands, I'm not. So here I am, bitching that I don't have space for more, but I can't spend them in battle because I don't have enough to spend on non-mandatory battles. Sure, I could probably get away with it, but with the time for the battles and running back to a Heart Block, what a waste. Why even bother. I'll stick with my half a page of Standard Jump and suck it up. Won't get anything good from loot after a battle anyway.
We're now avoiding combat and collectibles simply because of game design. Now the enemies on the overworld. They move faster than Mario vertically, he doesn't jump high enough to pass them horizontally. Shit will happen. You will get in battles. You will get a meaningless first strike. You will run. It may not work. You'll take a turn of damage.
We're now avoiding combat and collectibles based on game design, while also being forced into an unenjoyable combat system because of the same game design. And you know what, we're gonna run in circles doing this trying to find a Poison Mushroom sticker, or a Bowling Ball sticker, or the Scissors, a Fan to move the windmill, because of some stupid puzzle concept that is based entirely around burning a 2x2ish grid off your bursting-at-the-seams sticker album for a (nearly)one-off item you'll never want to use because it was so impossible to find, up to the point where you'll probably not work out when to use it(except for the Bowling Ball, that one was kind of a given).
We're now avoiding combat and collectibles based on game design, while being forced into combat by the game and being forced to collect by the game. Now, because of segregated levels, you can explore a bit! Ooh, how exciting. Except if you do World 2 and 3 at the same time. If you get stuck in World 3? Do you need a stupid real-world object, are you just missing something, or do you need to go through 2? Do you waste hours looking around for things, or do you just sit there and wonder why they even let you go out of order if you can't go out of order? What's a world map if I still need to tackle things in a perfectly straight line?
So now we hate combat, we hate collectibles, we hate the no-hints puzzle(here's a square on the level, fill it in with something, you might even get it right!), we don't understand the world map. Yet all of those things are jammed down our throats.
But I mean, yeah, the almost half a game of writing I saw was pretty solid.
https://www.reddit.com/r/3DS/comments/19w5p1/i_just_finished_paper_mario_sticker_star_and_i/c8rxzhh
Incidentally, much like how the game provides no incentive to seeing the end of the game, it provides no incentive to even fight the enemies along the way. Battles no longer reward you with experience points, as the only means of improving your stats stems from beating chapters and finding special hearts. Instead, winning fights rewards you with coins, and the occasional sticker. Coins are used to buy stickers which, apart from being found nearly everywhere for free, have one main use; to be used in combat. But since only a handful of fights are actually mandatory, it makes one wonder about just avoiding all the fights and keeping whatever stickers were lying around. You can even still earn coins just by beating a chapter in case you were worried about not being able to fund the in-battle slot machine for when you actually do have to battle. It should never be a viable strategy for the player to skip a primary component of the games content.
http://www.goombastomp.com/features/paper-mario-sticker-star-review/