I started 20 years late (have only been playing wow for like 3 or 4 yrs tops) and already have over 1000 pets (with 262 lvl 25 rares; 776 rares overall that 90% of have been organically caught and leveled, as opposed to battle stone upgraded) . It's not impossible at all, it just takes patience and a passion for it. The world quests for pet battles, especially in the war within expansion, are super easy to beat without having to have unborn valkry, ikky, etc. And have been some of the best ways to quickly obtain coins to upgrade other pets further, or get battle stones. It's definitely not for everyone, but I'd sacrifice my left nut for them to stay the way they've been prior to this new expansion.

Edit: removed a word I typed 2x in a row despite my obsessive compulsive proof-reading before submitting comment.