It can increase the trust and even help, but the current regulations (or attempts) are damaging the crypto reputation more than anything else.
I'm in for the betterment of crypto in the eyes of the masses but I can't see how or why regulations are damaging the reputation of crypto? IMO, these regulations are actually helping the crypto scene to mature and to prevent illicit activities which is widespread up to now. There's more good done than harm this time, and a short-term strike is rather acceptable rather than no negative effects yet the problem is still there.
In another hand, accepting to be regulated may lost the credibility of any project.
Why so? If people see certain projects that are regulated, they will have some kind of confidence in investing knowing that the said project is somehow recognized by the authorities and if the team behind the project failed to comply to their promises, or have ran off with the money, they will still have some form of ace against the perpetrators of the scam. Assuming that most ICOs and projects are registered and regulated, the only people who will ignore those are the money launderers and con artists.
In terms of trading volumes, in my opinion it will be just related to what I was saying above. If more trust are put in cryptos, more people will buy, so more volumes and so higher prices.
Again, regulations seem to be bad at first. Effects will be seen in the price drops, and that will only last a couple of weeks or months depending on how well the media sensationalized such events. Afterwards, it will feel more legal and investors feel more protected knowing that pump and dumps, exit scams and shitty ICOs won't ruining their bankroll and money. Aside from that, money launderers would stay away from doing the same projects with just different names and whitepapers knowing that they could get busted in the process. Overall IMO, this will do more good than bad in the long run, assuming that every regulation imposed towards cryptotrading is fair and just which, so far, is good.