Even when using that 7 days exception to classify STR income as non-passive, it still can't go on Schedule C, it still goes on Schedule E.  The difference is that the tax loss isn't limited by the passive activity rules on form 8582.  Most professional tax software (including all the Intuit professional software products) have an option to specify that rental income is non-passive, and that will cause the Schedule E tax loss for that activity to bypass form 8582.  That's how you do it, not by putting it on Schedule C.   

Yes, there are many tax professionals, who think that STR income goes on Schedule C.  That is a very common misconception.  

The instructions for form 8582 have a well written explanation of it, so I would recommend reading the "Rental Activities" section of that for a clear explanation of that.

If you want a technical tax code-level explanation, when a rental activity has an average stay of 7 days or less and the taxpayer materially participates, then it is no longer defined as a rental activity under the passive activity loss rules in section 469 of the tax code.  But that only applies to section 469.   It is, however, still defined as a rental activity under IRC 1402 and 1.1402(a)-4, which excludes it from being subject to self-employment tax.  Self-employment tax is the defining differentiator in separating activities between IRS Schedule C and Schedule E, and that's why the instructions for those forms specify that rental activities without substantial services don't go on Schedule C.

There are only two situations when rental income can go on Schedule C.  One rare exception is for a real estate dealer (such as someone flipping houses) with some incidental rental income. The other is substantial services (such as daily cleanings *during* guest stays, which is not typical).  The treasury regs and tax court cases get into many specific examples, and it's well defined at this point what circumstances qualify for substantial services and which don't.  There can be some gray area in rare situations, but usually it's clear that 99% of STRs don't meet the substantial services test.  

I can also list tax court cases confirming this if you would like (I just don't have that list in my notes at the moment).  

You also mentioned rental arbitrage, which is somewhat more of a less well defined area (there are some tax court cases, but they have some additional factors that make it unclear if they can be widely applied), but usually the guidance on that is it should also go on Schedule E.