I have no idea how/why Intel got a second life after that, but they did. Which is a shame. A sane market would have punished them and we all would have moved on.
For the same reason the line "No one ever got fired for buying IBM." exists. Buying AMD at large companies was seen as a gamble that deciders weren't will to make. Even now, if you just call up your account managers at Dell, HP, or Lenovo asking for servers or PCs, they are going to quote you Intel builds unless you specifically ask. I don't think I've ever been asked by my sales reps if I wanted an Intel or AMD CPU. Just how many slots/cores, etc.
The arm twisting gets them through rough times like itanium and pentium4 + rambus, etc. I still think they can recover from the 10nm fab problems, even though they're taking their sweet time.
Cray tried to build the T3E (iirc) out of Alphas. DEC bragged how good Alpha was for parallel computing, big memory etc etc.
But Cray publicly denounced Alpha as unusable for parallel processing (the T3E was a bunch of Alphas in some kind of NUMA shared memory.) It was so difficult to make the chips work together.
This was in the Cray Connect or some such glossy publication. Wish I'd kept a copy.
Plus of course the usual DEC marketing incompetence. They feared Alpha undoing their large expensive machine momentum. Small workstation boxes significantly faster than big iron.
A decade or so later on, they more or less recreated the architecture but this time with 64-bit Opteron CPU's in the form of the 'Red Storm' supercomputer for Sandia. Which then became commercially available as the XT3. And later XT4/5/6.
Imagine a future where Intel and Apple both adopt DEC and Alpha instead of Intel HP and Apple IBM.