asdf handles tools, not really packages. So asdf would install Python and not Python packages.
The other 2 reasons are more subjective. The first being I've had less issues installing packages with PDM. It's been a while and I don't remember which specific packages Poetry struggled to install, but my takeaway was just that I don't run into those problems with PDM the way I did with Poetry.
The other larger/more consequential reason is the maintainers of Poetry. There have been a number of GitHub issues replies laying out plans for things they will/won't do with Poetry, and it didn't inspire confidence in me. I want to do things the "Python way," not the "Poetry way," and PDM adheres more closely to the direction the Python project is moving. I don't want surprises later down the road when a tool (Poetry) is doing a bunch of custom stuff that eventually may not be compatible with the ecosystem at large.
All that being said, I had a lot of good things to say about Poetry while I was using it, and I do understand why people make it their package/project manager. Just wasn't the right fit for me.
asdf.vm together with pipenv is my go-to for Python environment management.
[0] https://pip-tools.readthedocs.io/en/stable/
As for Poetry, it is constantly improving and has gotten very popular. It should not be dismissed, especially for larger projects since its dependency management is so much better than pipenv. This is a good primer: https://diegoquintanav.github.io/poetry-primer.html
I think it’s fair to see appeal in poetry, but ultimately the maintainers have created a culture that feels a bit too non-collaborative to outside ideas or use cases beyond what they more narrowly envisage. That said, my perspective may just be tainted by multiple poor experiences interacting with the maintainers.