I finished typing up the post right before class started on my phone, so I guess I should clarify a bit more.
Campaign Mode is the only place the "pay to win" stuff exists, you can do everything else in game without any such limits. (Unless DLC characters count.)
People are upset about Story Mode for a completely different reason. (It's basically text summaries and fights, with voiced text summaries for the prologue and epilogue for each part. People probably expected more based on the Naruto games they've done.) There's items you can use there too, but they're "bought" using the points you get for beating Story Mode fights.
Versus is a completely different mode (Online matches are under Versus) and the only connection is that you can use your alt costumes and customized poses/quotes/sound effects there too, I think.
Campaign's recharge time was originally 20 minutes per bar, even in Campaign Mode, but they changed that last Friday. If you're not playing Campaign or the system is off it's still 20 minutes as far as I can tell.
But Campaign really is perfectly playable even with buying anything since the change to the 5 minute recharge, at least when I play it I do enjoy it. Not all the events require energy to participate, and some give you items/energy for free. The items are mostly pointless in my opinion, outside of the Boss chance increasing ones I guess. (I haven't used any, the fights are pretty easy 1 round matches.)
If you choose not to participate in any events that require energy and only do the bare minimum of damage to any bosses you face it's probably possible to play for a while before running out of energy. Mostly because you can only do two to three fights at most before a bar is refilled (An all S rank fight takes around 2 minutes) and the event giving you one bar of energy after a fight is pretty common from my experience at least. The only real issue is that beating bosses this way will take forever, since the easiest bosses require a few bars of energy to drain their HP in just one battle while some of the hardest take at least two battles even when using a full battery against them. (Boss HP in this case is a separate meter than their HP in battle, beating them in just one battle takes off however much HP you sectioned off using your battery bars. When you completely drain their HP you get some extra items, and I think you get items after you've taken certain percentages off of their HP.)
Also, Kotaku already covered
this twice.
They've definitely heard the complaints and are responding to them, obviously with the change to the five minute recharge while playing Campaign and giving away the first non-launch DLC character. (Although that's attributed to good sales.)
(Poses, quotes, and sound effects are used to customize your taunts, match intro, and victory screen. Every character has their own sets as far as I can tell.)
I don't understand Japanese, so this is mostly based off my experience and what I've read elsewhere.