Magnetic tickets are already slower than IC cards, and are both more expensive to produce and harder to recycle than QR codes printed on regular paper.
It is true that they are expensive to produce and hard to recycle, though, so it’s a good idea overall. But I’ll miss this iconic experience (or hopefully they retain it on some lines at least). (Edit: or just make the whoosh! readers work with QR codes! :)
Another cool thing about the paper tickets is that you can supposedly insert them stacked (i.e. both Shinkansen and regional transit ticket at a transit gate), and the gate will figure out which one to eat and which one to hand back to you!
And yeah, the ticket unstacking feature is really neat! (and probably it’s one of the reasons they want to replace the paper tickets – it’s a pretty complex machine on the inside :-)
I also retained all the Shinkansen seat reservation tickets (特急券) back when I had the old-style JR Pass, where you always had to enter/exit stations with help from the station attendant - and not use automatic ticket gates. I haven't tried the current style of JR Pass (since maybe 2022?), but I imagine that the exit gate would eat your seat reservation ticket, just like if you had bought the ticket in cash.