I don't see many use cases for the strict mode.  It is not strict enough to be used for validation, and while parsing HTML I can't think of any other case where I would want an exception raised (always as long as what is parsed by the tolerant mode is a superset of what is parsed by the strict mode).

If the parser is still able to parse what it was parsing before, I wouldn't worry too much about backward compatibility, because I can't imagine a valid use case where people would want the parser to fail (maybe someone else can?).