This would be a security nightmare for them. It is pretty normal for universities to have some sort of identity managmemt system that automatically provisions emails when you are employed there and deprovision them once you are gone.
Most universities use a portal of some sort for easy access to personal information and preferences anyway, so it shouldn't be too difficult to limit access for alumni to only allow them to change a few personal details like name / address / phone number and the like, plus email forwarding settings. I think the extra cost is negligible compared to what universities already spend on alumni like newsletters, conferences, dinners, etc.
If you forward emails automatically then you'd lose this accreditation. I suppose the solution would be an accreditatiom domain that forwards to your uni address only, but that's extra work now.
Additionally, making people who want to cold email work a little to acquire the current email address is actually a good thing, especially if they want to talk about something years old. I’ve generally had a lot more pleasant and engaging correspondence with people who worked out my email (say from a side project I develop pseudonymously) than ones who directly lifted my email from my professional profiles. So, expiring emails in papers generally isn’t a real problem anyway, and it’s basically never a hurdle if your target is still in academic circles. It only becomes a problem in this specific context of automated authentication (based on something not intended for that purpose).
Obviously our university isn't gonna make a 10k€/month contract just because some prof wants their mail forwarded to gmail. Especially not if they are not working here anymore.