Shimmering statue is a huge nerf. If health was as important as attack, it would be much worse than even the current steam forge. And attack buff is better than health buff (and has more synergies, like tiki reveler). Your proposal would be unplayable. The 4 health taunt structure is at least hard to deal with for rushers (especially Y), and the heal offers some utility against rush and burn. Shimmering statue also currently sees some play along forbidden library.
Cartographer is a huge nerf, and overlaps more with explorer. Triggering a deathwish is not hard at all and explore gives more value than your card proposal.
Court Jester : you gain the value right now, but you lose control about what to buff, especially buffing haste or pseudo haste creature to use them later as an answer. Or simply big threat like battle rager who become much more threatening at 5 health, but that you can’t and don’t want to play right away. And court jester is not an underplayed card.
Plague bearer is an interesting change, but a huge nerf. The ability to deal damage from accross the map is very valuable, and you can build your deck accordingly. And 2/1 supports the angry archetype, and makes it much easier than 2/2 for you to trigger it, with falcon dive or famine, if needed (along possessed ursu, or just to clear the board)
Fortune hunter should be punishable by ground shaker. If you want to play around, you can play tiki piper.
Prairie yak : great, you put a cheap early harvester into the efficient range of common removal. Not all cards need to be flavor. Let some be just stats. (The idea of last wish create a prairie is not bad, but we need a diverse selection of raw stat card, prairie yak being one of those).
Tax collector loses combat synergy and becomes very situational. The new card looks interesting, but the current one is good (both design and stats wise) and does not need to be removed from the game.
War Yak : interesting change to a card which does not deserve to be removed from the game. But, I am against neutral lands related buff. Neutral should only grant you more lands. Also, i t would be OP : how does it compare to oak father?
Siege engine : Artificial enforcement of structure synergy, while deleting a subpar but interesting card which does not deserve so. If structures are bad, such a siege engine just won’t see play. If structure are good, it still won’t see play because worse than than current SE, worse than boulder thrower and worse than yakapult (structure oriented decks already go up to at least 3-4 spec lands anyway).
Explorers : significant nerf to a barely playable card. How does it compare to Lore thief and biomancer?
Sharra : huge nerf. Also, with such stats, she should be renamed, well, I don’t even know, maybe towship slayer? Boar slayer? It tells a lot about the many cards that are at 6 health, thus why at 5 attack, there would a lot of things she could no longer kill (in one strike). Plus you’re destroying any cost 7 potential synergy. Sharra’s ability is not something you want for cheap, it’s something you potentially want to buff, with embrace and what not. I think she is in a fine spot rn, no need to nerf her.
Steam forge enforcer, similar as siege engine, you’re destroying a useful card which does not deserve so for an artificial synergy. It should at the very least be attack buff if structures are present, but current enforcer is completely different (used in rush) and much better.
Walking Forteres : meh. Huge nerf.
The point of overcosted neutral cards is to be able to play them early, and far away, usually in the face of your opponent, sometimes in double collection. If you nerf them beyond the point of playability for some artificial synergy, structure is about the worst synergy pick, because by the time you have 2 (decent) structures on board, you got a lot more colored options, that are better even without the artificial synergy.
Once again, beside the structure synergy fetish, it looks like you turn exotic situational cards into generic bad cards.