Why not He drives everywhere? Although, reduced to that the Englsih means as much "he drives everywhere (he normally or otherwise goes to)" as well.
If you think of the word "Strecke/Strecken" as "stretch or leg of a journey" you would get a better sense of this phrase. I.e. "Are you going to take turns driving to France? No, my husband will drive all the legs of the journey." or ..."You take this stretch and I'll drive the next." At least thats how my German parents would have used the word "Strecke/Strecken".
Because that would be Er fährt jede Strecke.
"every" (jed-) takes a singular verb and looks at all the elements of a group individually; "all" (all-) takes a plural verb and looks at all the elements of a group collectively, as one big whole.
They're not quite interchangeable.
I do realise that Strecken is plural, but my translation "He drives any distance" should imo be marked as correct. I was corrected to "He drives all distances". They both mean the same thing and my translation is the one most likely to be used, at least in British English. I can't know what Americans would say.
For this sentence it doesn't accept 'ways' as a valid translation of 'Strecken' but does accept 'paths', whereas I've just done another question where it's the other way round. I think 'routes' is a little less natural if you're british (which I am) so this is a bit irritating for me.
Not sure what I'm hoping to achieve with this post.