It's interesting, I think, that although some female travelers here like backpacks, a great many of the folks posting in favor of backpacks, and saying that they have no trouble carrying 20-25 lb. on their backs, are male. I suspect some men don't understand what an upper-body-strength advantage they have.
I turned my wife on to backpacks. She turned me on to the TLS Motherlode. I don't think either of us have packed 25 lbs going since our first, dumb traveler, trip to Europe. I suspect we're both under 20 going, and with booze coming back, I get over 20 (I always get to carry the bottles.
The thing about a pack that I really like, beyond all the mobility, is that it enforces a minimalist packing mindset on you. Everything you cram, you will have to lug. Thus, every ounce in the bag has a cost-benefit analysis in packing. This mindset is not for everyone. My parents, were they not somewhat infirm, could NEVER adopt this mindset. Even after seeing me and the wife cruise with carryon only backpacks... never. Mileage varies.
OP does not say when they are going in the OP. If it's summer/early fall, it's complicated. Zermatt, Grindenwald will want warmer clothing than everything in Italy, plus Paris and Amsterdam. If it's more November - December, the winter gear for Switzerland will be of use in Paris and Amsterdam, and of lesser, but still some utility in Italy. However, Venice rewards light packing like nearly no other major city in Europe unless you're staying in Mestre or by Santa Lucia.
I'd need to know more about the travel style, though my recommendation would be to try out a backpack and see how you feel about it. 4.5 weeks is a looong time to be saddled with a bag you don't like. that said, Rome, Amsterdam, Paris are all long stays, which won't require much bag movement. The Florence-Venice-Chur-Zermatt-Gindenwald portion... that's a lot of bag movement.