AFAIK TSV and PSV aren't specs, they're just an alternative delimiters for CSV. To that end most TSV and PSV parsers will be CSV parsers which match on a different byte ('\t' or '|' as opposed to ','). Which means if the parser follows spec (which not all do) then they will allow newlines and quotes too.
I'm not saying your use case is isn't appropriate though. eg if you're exporting from a DB who's records have already been sanitised and wanting to do some quick analysis then TSV/PSV is probably fine. But if you aren't dealing with sanitised data that doesn't contain \n, \" or others, then there is a good chance that your parser will handle them differently to your expectations -- and even a slim chance that your parser might just go ahead and slightly corrupt your data rather than warn you about differing column lengths et al. So it's definitely worth being aware that TSV and PSV suffer from all the same weaknesses as CSV.