It’d be fine at $4.
It would, except, as Donald X once said, "look, I can't make a Treasure that gives $2, has some other effect that is always beneficial, and costs $4; that's just better than Silver, and people by Silver for $4 all the time".
And then he made Delve.
The main problem with Silver-with-a-bonus for $4 (for games where people want Silver and aren't gaining it with a Silver-gainer) is that the pile just automatically empties. It's also not great that then you have that bonus in your deck, but didn't care about it at all, weren't making a decision there.
Delve has neither issue; it hits the Silver pile rather than a new 10-card pile, and those Silvers have no other abilities.
I don't know. If Royal Seal cost $4, would players drain the pile in most 2-player games it appeared? I tend to think not. The top-decking is not an ability that stacks, for one thing... i.e., having multiple Royal Seals in play confers no additional benefit.
They do not need to drain the pile to have an impact. Suppose you had a $4 silver with something like a Survivors effect. On many boards we would open with one each (e.g. boards with the good stuff at >= $5 or boards with a good terminal $3 and no other stuff we want at $4). We both play expensive engines (say Bazaar/Margrave) so we get a $4 hand and $5 hand on the second shuffle (the most likely outcome), so we each get another of the $4 silvers. On the net shuffle we expect one ore $4. Now we pile out the villages and the draw. Than is just 5 buys for a win and $18 - easy territory for engines.
This sort of thing is very common. Sure you might be able to do something with gainers to avoid silver entirely, or cheap cantrips (like Conspirator) ... but most gainers outside of a few like Mine, Tman, and Hermit can get gain the super-silver easily as well. For engine building you normally will buy 1-3 $4 silvers.
And the big hurdle here is actually just buying 4 of them. It is very easy to get to 6 gains - just split a pile of +buys with your opponent. Getting to 8 gains - to pile out the estates, is harder and often telegraphed. This is worse because super-silvers will help you spike more super-silvers. Something like Iw will let you gain & then pay for the better part of another and as treasures you need only worry about dead drawing your gains to play them.
They will be a pretty nice accelerate of end game pile threats on many boards.
Worse whatever bonus you give them is something everyone will get with exceedingly rare exceptions. Say we place +buy on Silver. When would you not get a reasonably useful +buy at $4? Only when you already get it somewhere else. Again, being on a treasure makes it vastly less costly to utilize that bonus than most actions - no need to gain a village, no decisions about how to play the last action on your turn, and no real worry about buying more than your engine can support. Just get more draw and life is good (obviously limited draw like Lib, Wt, Jack, Menage, Diplo, Vassal, etc. are exceptions).
Cards this generally useful diminish the strategy space. It can be fun with something like Chapel that completely warps the game. But any standard bonus on a Silver is not going to play that differently from Silver. So the game loses strategic depth regarding whichever standard element gets put on the card.
Between less time before end game and a loss of strategic depth, $4 super-silvers seem to be less interesting to play than cards that just try more interesting things. I certainly would not give up Quarry or Talisman to get a simple Silver replacement.
I have toyed around with is giving Potion a bonus (we had good fun making it duration w/ +1 action next turn or trash a card next turn). This makes sense to me as Pots are often completely foregone buys on boards - buy exactly zero, one and often trash them after you no longer are buying more Alchemy cards. As a big pile, Pots don't accelerate end game. As something completely different (but useful), Pots are far less likely to be a brain dead buy. Of course I am weird and like the potion mechanic and wish it were more frequently used in Dominion.