Another idea that I think would be amazing is if the game was a phone app that used google maps as the in game map. Businesses could be pokemon centers, poke'marts, gyms, etc. There are so many possibilities in that area

Dude YES.

Pretty much anything could be 10x better if you slap mmo on it

Pretty much anything could just as easily be 10x worse if you slap mmo on it.

I'd find it fun and relatively easy to design a pet monster game, single player or mmo, with arguably better gameplay than at least the first gen games. But the problem is that as soon as you strip the pokemon name off and use original monsters people don't seem interested. I can kinda see why - the idea of turning (what was it, 8? 10? 12?) and being given your first pokemon friend to go journey around the world with is a strong fantasy, that people have a lot of loyalty for. But that's a clear part of the IP, you more or less have to change it around to be unrecognizable.

As far as designing a pet game in general, I think the big question one has to answer as a designer is what are the pets for? Are they for combat? Do they become units for an RTS or tower defense game, or workers for a worker placement game mechanic that feeds back in to the player's ability to capture/produce more pets? Are they sold for money in a tycoon mechanic? Are they for collecting? (Many, many pet games fail to take advantage of the urge of players to collect one of each pet; some games don't provide enough storage space to make this possible, others just don't acknowledge it as a gameplay goal or allocate a reward for completing this overall goal or the substeps of it, and I think there's no easier way to frustrate the average fan of pokemon-like games.)

On a side note, this thread reminded me that the pokemon yellow was probably the game that first got me interested in game design on a basic level. I remember I used to try to make my own pokemon cards lol I had so much motivation and time on my hands back then. If only I had the knowledge back then that I do now...

I know exactly what you mean about non-pokemon monster games though. I don't know why but I could probably never get into a different pokemon type game, even if it were as good a game. But also, I lost all interest in pokemon after the second generation for whatever reason. It was probably part of a stage when it wasn't "cool" to be into it