With some of the anomalies/ other effects that put a card in your hand it’s a poor oversight to let those get lost by a full hand instead of spawning when room becomes available like spellcrafts. Penalizes playing builds like quilboar that spawn mass gems and doesn’t give you a chance to spend before getting card / rewards.
What you are describing is what is usually called “Playing Greedy”
It comes at a cost usually and you are describing it perfectly, the tax you end up paying when playing greedy like having 10 blood gems in your hand at the end of your turn, keeps you from any other cards such as rewards from anomalies, Duo giving you its end of turn copy, the magnetic freebies, etc. SO long as you play greedy, you will end up blocking yourself from your own progress in this way.
But the idea is that is an acceptable cost for the amount of greed you are engaging in. Ideally, the blood gems ought to outweigh anything you might need to have made room for otherwise. If they aren’t, then I suggest dont play so greedy and leave room in your hand then.
They have actually done a great deal of change in the last minion shakeup to stop this from happening to Quillboars. It used to be common place to obtain far more gems than you could hold. There’s only a few ways to get them in hand now and those are usually early build minions that you drop later.
What you’re describing is no different than being board locked. You want to play a minion and/or keep it on the board, you’ll have to sell one. It’s the way the game works.
If you want to add more to your hand or be able to do so, then you need make sure a slot(s) will be available. If you have too many blood gem generators, per your example, you can sell them off. If this hurts the build, you’ll have to determine if your progress values the generators more or what you want added to your hand. Again, this is just how the game works.