Is there a danger that protections in place to protect the composers, publishers and performers of songs - are in danger of generally preventing us from being able to sing or of seriously limiting what we can sing and where?

legally, in the US, it already does - unless performance fees are paid. Luckily they have pretty well ruled that the responsibility for this lies with the VENUE; which is why some venues ask that your set list be restricted to your own or public domain /trad/out of copyright items.