i think it comes down to two things. personal preference, and the focus of the site.
the majority of pokemon sites seem to focus on the theme of adventure that the world has to offer. staff moderated pokemon spawns serve two purposes.
1. ensure the player doesn't immediately walk in and walk out with the rare pokemon of their dreams
2. help players to level up their pokemon for future events/battles
you've mentioned already that you don't want to have levels and stats, so that answers the second part of the question already. that leaves you with one purpose - modded pokemon would strictly be to help ensure that players are fair when building their parties.
does this seem necessary in your case?
i have written at many pokemon sites through the years, and the one i was most active at - by far - the majority of my 200+ posts were responses to group wild threads. and i have to say, i didn't enjoy them one bit.
occasionally there was the great interaction, a real adventure from having random pokemon thrown at you, but the majority of the time? i noticed players (& me too in some cases, i'm just as guilty) going out of their way to ignore or shut down my character in order to focus on the wild spawns - which resulted in zero development and honestly? wasn't much fun for me! of the couple hundred posts i did, going through them all, the most fun i had was in threads focused on interaction rather than rng pokemon and grinding out attack posts.
long story short, i do not consider rng wild spawns a necessity for pokemon sites, and in truth, i'd love to see more that move away from this system.
as for alternative ideas, listing the wild pokemon in each area and letting players determine their own threads seems like a good answer to the problem. if they want to battle, catch, or study, they know where to go, and it doesn't require staff at all. you could even have limited time events where pokemon appear in swarms, or in different locations, or their regional variant arrives - but none of it would require staff to sit there and roll dice.
if you want to keep mod threads, and just lessen the number, having players purchase modded threads for more significant events or the surprise legendary visit could be fun a way to go. purchasing modding for gacha rolls might be - ... harrowing for players on both sides. xD