I feel like you are over-valuing her gameplay.
I heal whoever has a giant red cross on their name and don't really prioritize the order because it doesn't usually matter. In a frantic moment, Ill probably heal squishies first, but Im really just holding down a button and keeping meters up.
Soldier is not much more skilled, but his ultimate at least requires some thought-- positioning, targeting, and timing. Mercy's is not the same at all because hers is simply to zoom into the skulls and press a button. Mercy doesn't need to target anyone in particular, and really doesn't even need good positioning or timing.
She can time a 4-hero Rez, but she's just as able to target a 2-hero Rez and do well enough to turn the tide.
Mercy is picked because the rest of the healers suck ass at healing as well as she does. If the enemy has a mercy, you best take a Mercy yourself or else you are at a disadvantage and will lose.
So Mercy just ends up being a boring, stale, and brainless character that has to be taken by someone who is willing to put their need to win over anything else.
If youre not prioritizing healing targets then youre not playing mercy right, and the fact that you didnt mention damage boost is telling. High level mercy's are conatantly switching between heal and damage boost and knowing when to do so isnt easy. Damage boosting at the right time can make or break a duel between a teammate and an enemy.
Also, you are hilariously underselling the importance of good rez usage. Rez is one of the most impactful ultimate in the game, which is both a blessing and a course. If youre playing against decent players, with decent ult management, you aren't going to get many opportunities to get a huge 5 man rez, and when you do, you are often bringing your team back into a disadvantagous state.
Example: enemy Reinhardt shatters your team they get wiped ---> 5 man rez----> enemy zarya gravs your team ---> wipe #2 ---> cry like the useless mercy you are.
Mercy is my most played hero and ive gotten to masters with her (with > 50% winrate) and I'm still not close to managing my rez. In a teamfight I have to consider when to rez and who to rez, which include who on my/the enemy team has their ult, and where theyre positioned. Also, while mercy's invulnerability is an overall buff, sometimes you have to choose between ulting to save yourself, or saving it for a better overall rez, which is a risk in and of itself.
Also, the fact that mercy's rez is so impactful makes her the highest priority target in most teamfights, which means genji, Eva, Winston, tracer, reaper, pharah, sombra (characters incidentally part of the most popular comp atm) are all hunting you down. At high elo, people dont forget to go for mercy. Being the highest priority target means that keeping yourself alive is more immediate and important of a skill for a mercy than a Lucio or a soldier. Most other characters, basically.