There is an entropy card with that ability. Usable multiple times makes this OP.
I highly disagree. Look at the Nymphs.
Nymphs usually have a relatively high initial cost that can spam the same alchemy card for a lower cost. They also deal damage (many of them are usually quite strong). They are vulnerable to CC. 1 per turn per nymph (barring SoR)
This has a relatively low initial cost and a repeated cost that can spam random alchemy cards for full price. It does not deal damage. It is vulnerable to PC. Multiple times per turn.
Nitpicky-wise, Nymphs also leave your handspace open (+Fractal, Draws) while this clogs it (+vs. Nightmare, +vs. enemy SoBr). Nymphs are epic rare, but that is pretty much just a novelty, as they are not epically powerful (else it would show in the meta).
This might need a price increase, it might not, though I'm leaning towards +1-2 initial and +1 Activation. But it is far from being overpowered. The extra cost per card and random nature of it makes it far less powerful. As for the comparison to SoSe, SoSe makes three cards once for cheaper (significantly if this gets it's cost increased) from any card in the game (always including 1 entropy). However, the Alchemy cards alone can rarely win a game for you
A deck built around this would be extremely vulnerable to PC, Quanta Denial, OTK, creature spam to outpace the CC, or stall decks. I very highly doubt it's overpowered. Additionally, diminishing returns with multiple copies as being able to activate it multiple times makes extra draws worthless if your opponent didn't bring PC (and if they did, well, you're ruined anyways).