It isn't "exactly impossible" though, it never is. You can find out a more efficient way to create it, or you might have more power available in the future.
All manmade elements have been extremely expensive to make the first ti-me, and that hasn't stopped them from being constantly used.
There is no efficiency - juste pure energy needs. You cannot probe a quark with lower energy.
Then there is nothing to use from such experiments. The research is purely academic, it is not like the cure for cancer is hidden behind a gluon.
I can understand dumping even 20B€ in research which brings something tangible. Making sure that the structure of a quark is what we think it is is not one of these.
There is certainly efficiency to consider when making energy. We can't tap into the full potential of any source, there are "hard limits" to many of our current methods, but that doesen't stop a paradigm shift from happening and making it so.
Many things studied before had no "tangible" use then, it doesen't come like that. It's iteration upon iteration, using previous work to achieve a little bit of something new. You cannot foresee the future beforehand.
At some point in physics there is no "paradigm shift". In order to probe such structures you need an enormous energy. An energy you have to build an accelerator to have.
What do you get in return? The confirmation or not of a theory which can be confirmed only at these energies. It is not as a non-confirmation would turn around physics, it would be just some strange thing happening at these energies.
Compare this with experiments from the late 1800 and early 1900. You had obvious holes in the theory (Michelson-Morley, the ultraviolet catastrophe, ...) - these experiments were showing that something in our everyday theory is wrong. Not some fluctuations at 20B€.
There are branches of physics where the research is really cool (notably solid state physics) and which you can make a real life use of. Particle physics is not one of them.
As I've been saying, you don't know the point at which there is no more to learn. Even minor things can have major impact when combined with further research.
Things like "enormous" are subjective, and it's indeed not impossible to get such amounts cheaply in the future, even if you can't at the time reduce it's need.
It's easy to look in the past and point out the obvious when you already have all the answers, but trying to divine something that changes the way you think about current physics is not as simple.
Things like "enormous" are not subjective in physics. We know that we need a certain density of energy to probe a particle. There are no miracles: it has to come from somewhere and it is not like there are sources of such energy that can pop up from nowhere. We simply do not have a place to harvest such energy on the global scale, and we know we won't have anytime soon. There are simply no sources for that.
> Even minor things can have major impact when combined with further research
We are talking about things happening at energies which are way beyond normal interactions. Let's imagine we pick a simple artificial signal from the sky, from a place that is 5000 light years away.
People will get crazy about aliens and loose their shit on how we are not alone. And so what - from a practical perspective there is exactly zero interest in this. We cannot use that information at all because whatever is there is unreachable.
There are however plenty of place in physics which are worth the effort (I mentioned solid state physics as one of the most promising ones). Not to mention biology where we are only right at the beginning and there are plenty of outcomes.
If we had infinite resources then fine. We do not have them. And putting 20B€ in some fancy research with zero practical interest (such as this one, or middle-ages French literature, or Platon philosophy, ...) is a tremendous waste of opportunities.
I understand that we need to fund research with no practical interest - this is part of what makes us human. Just not 20B€ when people are starving, dying, etc.
All manmade elements have been extremely expensive to make the first ti-me, and that hasn't stopped them from being constantly used.