Why some Azerite powered gear cannot be sold to vendors?

Solution 1:

It is speculated that azerite gear lost its gold value when patch 8.1 dropped to ensure players would scrap it instead of vendoring it. As of patch 8.1, scrapping azerite gear greater than or equal to item level 370 rewards you with titan residuum, a currency you can use to buy high level azerite gear. If you are interested in M+ or raid progression, the titan residuum from scrapping pieces of azerite gear should be far more valuable than 50 or so gold.

I imagine this helped the support team avoid a large number of tickets requesting residuum for mistakenly vendored azerite gear.

If you no longer need a piece of azerite gear, feed it to the scrapper. There's no need to hang on to it.