Ajani's Pridemate is basically a white Tarmogoyf. The speed with which the little bugger can grow is disgusting, and while it doesn't immediately come out as a 4/5 if played in the lategame, I feel like a much better base body and limitless growth should make up for that.

The actual challenge is in finding the incidental lifegain. Ajani's Pridemate works well in the early stages of Magic Arena, because the white weenie deck that's easy to collect from commons has a lot of incidental lifegain. It's almost playable right now because of that, but the top decks just race white weenie or crush them too early/easily for them to gain that traction.

I think coming down late game as a real threat is probably more important than the small increase in base stats and lack of an upper limit. 90% of the time it won't get bigger than the Goyf could before the game ends, especially if it came down late.

He's a mainstay in a lot of Soul Sister builds. I'm not really sure where else he would fit into Modern though.

Ajani's Pridemate isn't comparable to Tarmogoyf:

1. The turn Ajani's Pridemate comes down, it's a 2/2 Grizzly Bear.
2. How are you going to gain life? Healer's Hawk isn't playable in Modern.
3. Even if you can gain life, you need many turns before Ajani's Pridemate is as big as Tarmogoyf. With Tarmogoyf, you don't even have to do anything before it starts growing (since the things you have to do to grow Tarmogoyf, like play Thoughtseize and fetchlands, you already want to do anyway).

There is one deck that plays Ajani's Pridemate, which is the Soul Sisters build that utilizes Soul Warden and Soul's Attendant. That way with a sister on the battlefield, Pridemate immediately starts at 3/3, possibly more. The deck is playable, but T2 at best, closer to T3, since it doesn't do particularly powerful stuff, it doesn't generate a lot of value, and it's synergy-driven with all its key cards dying to removal easily (e.g. Fatal Push / Lightning Bolt on a sister means Ajani's Pridemate is back to being a Grizzly Bear; Fatal Push also kills Pridemate regardless of size).

It can be a good card, but only if you play bad cards.