Sure, would be nice to see the NHL up to 125 or 150, but realistically, never going to happen. It would take massive land acquisitions to get that, and at that point, you'd be better off building a whole new right of way. FWIR, the tracks are too close to allow for proper full tilt into curves, the signal blocks would have to be altered, and MN has no need to go anywhere close to that fast and they are the ones who maintain the line. I believe they had a stretch of 90 mph track that they did cut back to 79 mph so they didn't have to keep the track in a higher class for just a couple miles. 79 vs 90 mph on a commuter train doesn't make that big of a difference anyway. Now if Amtrak owned the NHL, then perhaps they would have different plans. High speeds has never been the NHL's forte... that honor has gone to the Shore Line since the 1900s.
New Haven to Providence via Hartford? That hasn't happened since the NHRR days, and there probably never was such a direct service. Hartford to Providence would require pretty much almost an entirely new right of way. The existing line which is now a rail trail from Manchester to Willimantic has quite the curve in it, traveling north then looping back south to go east... blame the topography of the region. New Haven to Boston via Hartford/SPG is more realistic.