The ‘single invariant timeline’ theory has a name; it is called the Novikov Self-consistency Principle.
Some other options are 1/the boring option, where no time-travel at all can occur;
2/The rewrite option, where time is rewritten, and the other timeline ‘ceases to exist’ (where does it go?) and 3/ The many worlds option, where the new timeline that is created is just one of a myriad other alternative timelines, some of them created by time-travellers, others just occurring naturally.
The bizarre ‘Back To The Future’ timeline is a variation on option 2, where the changes happen slowly for no discernable reason, and entire histories are wiped from reality by careless timetravellers.