Even on the slow (by smartphone standards) Nexus One, Flash ran quite decently. The Nexus 5 is a good magnitude faster in every way (I can't find specific parity-version benchmarks, so perhaps I'll fire both of them up and give it a go), moreso in some ways like the GPU, and is as powerful as some desktops that people still use in business settings. It would of course have no problem with Flash.
Flash failed because a good percentage of existing content relied upon the accouterments of a desktop, namely the keyboard and the mouse. Minus these it just made for a frustrating experience for a lot of users. Add the fact that sites were loaded with obnoxious, taxing Flash ads, and it just gave users of Flash-enabled devices a very negative experience. It also reflected poorly on the product as a number of popular tech sites compared Android and iOS web page loading times, the former seriously hindered by the loading and overhead of Flash.
There were later changes to make it activate on click, but that just made it even more of a usability burden.
In a way, at the time this whole debate was raging, iOS users got to enjoy essentially a free "adblock" in the absence of Flash.
I have to entirely disagree with any notion that smartphones are underpowered: I am currently working on a very intense real-time image processing system and with each iteration I'm finding that I'm increasing the scope and featureset because the performance continually blows me away. Even when I work on "older" devices like the Galaxy S3, with good code and good parallelization (incl. the GPU), it is just a ridiculous platform.