The Beach Boys could have put together an entire baseball team of all the outside co-writers/lyricists.
Rock bands from the late 60s onwards was specified in the original post. Lots of pop groups in the mid-60s were recording songs by outside writers - in fact the majority of them were. The Monkees don't count, for example.
Richard cowrote some of the Carpenters hits. Blood, Sweat and Tears is another band that had a lot of covers but some originals.
Jeff Beck has way too many groups to list, and a couple of his albums list him as a main songwriter. I’d guess that way more than half of the songs, and maybe three quarters of the songs he’s released since the late sixties have been written by others though.
If you look at the Stones's early years, it is clear that they saw themselves as a "proper" R&B/blues band. Their goal was to turn on their peers to the blues and soul records that they were inspired by, Jagger is quoted in an early interview stating that "a British composed R&B number just wouldn't cut it". Of course, once Jagger and Richard put their minds to it, things changed - rapidly.
Not really. The OP mentions that most bands since the late 60’ s write their own words and music. Then he asks us to name which bands from the “rock era” relied solely on cover tunes or outside songwriters . Bands in any year of the 60’s qualify for the “rock era”.
I guess it was a hit in the UK. Being American I never considered it a hit. He certainly did not write a significant number of their songs, and almost none I ever care to hear.
Read the OP’s post and tell me where I’m mistaken? So, Cream in 1966 and Hendrix and The Who in 1966, etc., etc. aren’t part of the “rock era”? Were they part of the “folk era”?