I think the fact that many do not putt out hurts your handicap.
Also there is a little bit more involved in traveling and scoring well.
One factor IMO is when you play 80-95 % of your round at one course, you get pretty good, or 'comfortable' at all the shots required at your 'home' course. You know that 'right' is no problem, or you 'have' to be short of pin-high, etc.
In addition, you get a little complacent at reading putts. You are not generally honing your reading skills at home.
Then you play other local courses (maybe only once a year at a particular local course), and all of sudden, you are a little unsure about what will happen when your pitch shot goes onto the green. Suddenly all those 3 to 10 footers, where at home you know the break or at least know it will break only one direction, become more difficult to sink.
Just as a big general statement, I think newer courses 'tend' to have more water, maybe more O.B., given all the real estate courses from 1970s to 2000s, etc. While hazards are figured into the course ratings at each course, you might not know how the ball bounces or how it feeds towards, or maybe how it plays shorter toward a hazard, or how you can completely play away from the hazard and still make a par or bogey. You don't have the local knowledge for the hazards that really eat into your score.
IMO, and an echo from above, putting out in your usual game will be a great help. Remember to quickly putt out.