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You could consider the behavior of committing crime as evergreen (can you imagine an MTG set with no cards that target your opponents or their things?), but the keyword action itself isnt evergreen

You can, however, Stifle the abilities that enable the keyword action

You can play explore cards that let you hit your land drops more efficiently, it helps to play 3+ colors or expensive spells, it sets your graveyard for shenanigans, and much more

Whenever a creature dies, untap this creature

It's just hard to get as excited about a one toughness Tim when a format is filled with a billion and a half removal spells in the common slot, and where you can already be at five life by the time your Tim becomes active

Now you just need a way to convert damage into creatures, and there are plenty of ways to do that