I've time traveled in small increments to get the Able Sisters and the town hall. I don't like waiting for a day for something to be built.
I time traveled for 8 days to get my island homes together in the little "hotel" I had. There were no cons, and I'm really glad I did it since it got Beardo to move out. Best thing I've ever done tbh.
There's no real cons if you time travel in small increments other than your turnips spoiling, from what I've seen. Time traveling in large gaps (I mean a month or more) has various potential consequences however, but I haven't attempted myself.