As someone who has, over the years, cobbled together a song or two and made tunes for texts exhumed from dusty local history archives, here's my two penn'orth. I may stray off-topic a little!
When I sing a song someone else has written I always try to give credit where credit is due, something which on the folk/acoustic music 'scene' is fairly easy, although I have one song where I can only attribute the text to 'anon'. When it comes to the 'standards/pop'n'rock' world things get difficult-even with google. Even presenters of radio shows can shine through sloppy research e.g. they've never heard of Ewen McColl.
When I started song-writing, I was producing 'Mock-Traditional' style songs, along with many other better known writers. Hearing one of your own songs introduced by a singer as 'traditional' was a sort of accolade! A seal of acceptance and, perhaps, quality(?).On the other hand, it's nice to hear yourself being given the credit for a good song- unless of course, the other singer mangles it up completely!
As far as borrowing tunes is concerned, surely one of the reasons that the denizens of Seven Dials wrote to existing tunes was that it simplified spreading their songs among the populace. Coming home from market with a new broadside, it was a reasonable bet that somebody in the pub would know the tune specified for the song. And of course, an existing tune makes a useful framework when you're writing- the only problem is, some tunes, e.g.'Van Diemans Land', are so insiduous that it's well nigh impossible to find your own tune once the song is complete!
On stage, I rarely plug my songs as my own work unless they are tied to specific events or personal experiences. Ditto with tunes for songs exhumed from the archives.(I can think of one group in the UK who might be surprised to know where one of their songs actually comes from!) The town of Bakewell never knew there was a song about their witches until 2009, 35 years after I wrote it. Songs can catch up with their writer!

Don W.