What you're arguing is the entire reason for mobage transactions existing, not an actual tangible difference between free and paying players. Convenience isn't inherently P2W.
Look at it this way. If I showed you a random account with a sizable amount of non-event golds and a few rainbows (ignoring levels, affection, ampies, etc.), would you be able to immediately distinguish if it was a long-time, lucky free player, or a whale who picked up the game last Tuesday? No.
Or look at it in reverse. If I showed you an account with practically no golds or rainbows, could you say for certain if it was a new free player, or a paying player with an extremely unlucky streak? Still no.
Whatever gap you see between free and paying players is largely eliminated by time and luck. Paying mitigates both, but without the guaranteed deals, it's still up to RNG in the end. Again, the main reason for FKG's popularity in the first place is that freemium players aren't left in the dust. Ergo, not P2W.
Time is only a factor if it's not feasible for free players to "catch up" to paying players. See: Pero, Osawari, really any game with ranking events.
Time is not a factor if it's just RNG in the end, and there isn't even any pressing difficulty or competition. Again, even Nutaku FKG is friendlier than DMM in this regard. Yeah, everyone gets less free gems, but if they hold 11-roll guaranteed gold deals every month, that's already a boon for free players.
And to go into a depressing note, in the end, waifus are just an advanced form of cosmetics anyway. Games like Overwatch aren't pay to win for a similar reason. Just because you can pay to speed up the process of getting loot boxes, the only thing it does is reducing the amount of grinding you have to do. It doesn't give you a distinct advantage over free players.
Pay to waifu. Pay to dress-up. Not pay to win.