bitcoin would have been in the same place even if CME and others never entered it. the only difference would have been the fact that price might not have reached $20,000 so the drop may have been smaller. for example if CME never made their decisions last year, price may have gotten stuck behind $10k and with a lot of push it could break it and reach $11k then drop to $8k-$9k and we would have been right where we are right now. or with a little luck price would have been around $14k with the rally starting soon.
the current price has nothing to do with their "control", it is mainly thanks to how price moved last year.
we don't know that. We don't know well enough that we can say the market had little effect. Since up until now they can trade crypto with no regulations it is quite possible the CME and ETFs could be having a major impact