Cost/Benefit of transfering from Masters to PhD mid-program
Whether it is "okay" to skip the Masters depends on your country and field. In US institutions in most scientific fields it is considered the norm to go directly from Bachelor's to PhD (of course many people get a MS along the way, too, but it's not necessary). In my experience, though, even in countries such as China where enrollment in a MS program is generally required to get accepted to a PhD program, once you get your terminal degree, nobody cares too much about what came beforehand. 

Regarding whether it's worth your time, this depends on what kind of offer you're considering. Is the advisor strong in their field (regardless of the prestige of your institution overall)? Could you expect to publish two or more "good" publications ("good" is a relative bar, of course)?

In general, my feeling has always been that as a student, it is easy to "trade up," i.e. go to a MS program stronger than your BS program. Do a postdoc somewhere stronger than your PhD institution. However, once you leave the student/trainee portion of your career, in academia you are more likely to have to "trade down." The MIT and Stanford grads are enough to take most of the top faculty positions in any field in a given year. Therefore, if you want an academic career, you may put more emphasis on prestige. 

If you aim for corporate work after graduation, then being at a "better" institution will probably open you up to a better network of alumni who could help you navigate to a good entry level job that fits your skills, setting you up better for future success.

Trading those away would be worthwhile if you really felt that this position was (a) likely to give you academic output that could compensate for the potential future networking loss, or (b) if you felt like this was the best offer you were going to get, or were unsure about the possibility of future offers (i.e. a bird in the hand is worth two in the bush).