Does it make sense to plan travel days for Mondays?

I don't have an opinion about Monday travel, but I do have another question. Why are you backtracking? Why not fly into Venice? It's a much better city to acclimate to and get over jet lag. Why stay in Rome twice? Save Rome for the end of the trip and fly home from there. Flying into one airport and leaving from another is an open jaw or multi city flight. It can save you money and time to avoid the backtracking.

Not everything will be closed on Mondays. It's easy enough to see what days the places you want to see are closed.

Personally I would determine my travel days by deciding how much time I want to spend in each place, not by what day of the week I would travel on.

I agree about traveling open-jaw/multi-city and avoiding backtracking. I usually plan my itinerary by most efficient route and how many nights I want to spend in a city. If I have a long trip, I prefer to do that on a Monday, but if it's a couple of hours I don't plan a day around travel.

The other consideration is what I want to do. On a Monday in many cities, even if every museum is closed, churches will be open, and so will most archeological zones nearby. Wine and food tastings, or orientation tours of the city, also usually run on Mondays.

Check a good up-to-date guidebook or website to be sure.

All things being equal, we found Monday train travel to be advantageous, as not only are museums closed, but many shops as well. However, it assumes that your Sunday is well occupied as it can be a less dynamic day as well.
For a traveler driving a long way, Sunday is best because almost all trucks cannot be on the road.

Thanks everyone for your comments about Mondays. I am aware of open jaw but that will not work for us this time.

Mondays are good. Lots of museums are closed, so you might as well travel.
Sundays afternoons have the same issue (many things are closed), however trains tend to be packed with weekend travelers going back home getting ready for the workweek.

Mondays are very good days to travel for precisely the reason you think. I also try to avoid traveling on Saturdays, as that is usually the day of the week that's most often chosen for train strikes - the dreaded "sciopero" (pronounced SHOP-er-oh).