Bought a house where many of the ouside faucets leak from the t-shaped
screw handle at top.

Just wondering, is it worth "fixing" these?
If not, what's a good replacement strategy?

I would tend to replace them with the ball type with a nice long handle but
some of these leaky outdoor faucets seem to come right out of the
foundation with no joint visible. (Why do they build them that way anyway?)

Do you recommend "fixing" the existing faucet with the t-shaped handle?
Or is there a better solution?

For those faucets which come right out of the house foundation (no
screw-off fitting is visible), how are we supposed to replace them?