Not killing coppers directly is pretty irrelevant, being able to convert estates into Golds is extremely powerful; so much so that you will gladly grab a copper for the privilege. What is relevant is that the gold so ungodly slow that just about anything else is faster.
Aha, so Gold is extremly powerful yet also ungodly slow. Bit too schizophrenic for my taste.
Let's say it like this: Copper trashing is never irrelevant. If you cannot get rid of the Estates you still buy that Moneylender or that Baron and ignore Transmute. If you buy Potion for the sake of something else you still don't buy Transmute when you dud unless there is no trasher/sifter around and you really need a Curse trasher. Familiar games, there we have a niche for Transmute. Except for such rare circumstances it is simple bad, even if you could have it for free.
I mean, what more can you say. It is obvious that you somehow for some strange reasons love the card but objectively it is among the worst of the game. You can see that by the very simple fact that transmuting Coppers into Transmute is often bad which implies that the card is worse than Copper (or to be more precise, the net benefit of every Transmute beyond the first one is usually negative).
Mute is objectively the worst card in the game. It is too slow for what it does.
An inability to trash copper is not sufficient to doom a card. Rebuild does quite nicely without it. Jack does quite well without it. As long as estate trashing is coupled to something powerful enough, it is worthwhile as a to get that card.
Mute does not suddenly become good on boards with easy copper trashing. Say you open Counterfeit. All your coppers are trashable, when do you buy Mute? My answer is typically never. Spice merchant likewise has never tempted me to go Mute.
Heck, how often do you buy Mute with Donate? Copper trashing is trivial on Donate boards, but I have never seen an opponent go for Mute after they have a copper less deck.
Ultimately the real reason we know that copper trashing for something like Dismantle or Dev is less important than gaining off the estates is that you will virtually never trash a copper over bootstrapping your estates into better cards. It is far more effective on a hand of DCCCE to gain something even if you plan on buying a nice $2 (e.g. Squire). Nobody says, well I am trying to build a lean deck here so I will trash a copper rather than flip an estate to a gold and gain a copper. Killing coppers with Dev or Dismantle is a consolation prize when you cannot get the real value out of the card. After all, everyone buys these two on Donate boards unless there is something much more powerful around.
I mean seriously, suppose we "fixed" Mute by letting it flat trash a copper. Would you buy it then? You still gain Golds from green and duchies from actions, coppers just function like curses and go straight into the trash. All you have to do is burn your opening $4 on a pot, a first shuffle buy on a Mute and then you have a terminal trasher which gains gold and kills copper. And then once you play it, twice, on coppers - you are break even on card count. The third time you play it, on an estate, you then are starting to make headway with a deck better on cash density than you started with.
Even being able to trash copper would not fix Mute. It is so ungodly slow that you can just buy village/draw and come out ahead. Unless I am forgetting one obscure one, I would buy every single other trasher before I would buy a Mute that trashes coppers - it is that slow.
Sure trashing coppers would make Mute suck less, but that would not change how often people bought it. Game is over on most boards before a copper-trashing-Mute beats Trade route.
And this is what I like about Mute. It is a good object lesson for the price of SPEED.
Mute is slow, it sucks.
When Mute is faster, you can actually do something with it. Very few things give you duchy efficiency VP for a single terminal trash. I have won at least a half dozen games by snagging Mute when it doesn't suck because the stars align and I can get it for low opportunity cost.
Alchemist stack with a +buy? No buying power loss the turn I grab it. Every-other-turn after that I manage copper -> Duchy. That beats most non-attack terminal silvers.
Pool? Any $1P will be a Mute. Increased action density. Fodder for late game duchies. Golds instead of estates. This is all good unless I have some truly stiff competition for terminal actions.
Possession? Yes please, let me trash out all the treasures so you cannot buy provinces.
Vineyards? Spare +buy for an action worth 8/3 or even 4/3 VP after the Vineyards are piled? Yes. And trashing a copper becomes a no-brainer.
Lurker? Burn my Lurkers for late game duchies? Absolutely. I have won by Lurking a Mute on the final turn to take a 3 VP lead at least twice.
Forge? Forge EE -> Pot, buy Mute, Forge Pot -> Mill, Mute Mill -> Gold/Duchy; next turn Forge for Colony.
When Mute has actually worked (i.e. <2% of Mute games) it has not been when I could couple it with a copper only trasher but when I could get it without having to burn two full buys. It amazes me that highly ranked players won't Lurk for Mute when it is literally the only way to score more than 6 VP per turn on the board. This tells me that people don't understand why Mute sucks, just that it does.