It couldn't even handle unaligned access in it’s original form. Surely an architecture to last for 25 years.
The main issue people tend to bring up with Alpha is the very loose memory model, of the "things happen, but different processors may not really agree on the order they happened in" type of thing (plus, isn't it rude to want to know what other cores have in their cache?). Which would be a pain in our modern multicore world.
Of course we don't know how things would've evolved over time, ARM (at least on big cores[1]) shifted towards the forgiving model for unaligned access, it's possible over time Alpha would've similarly moved to a more forgiving environment for low level programmers.
[1] On embedded stuff, you're going to the Hardfault handler.