Not if it was paid for by a tax on rental income. 100% tax on everything over the equivalent mortgage payment on the property would be a lovely cap on rent values.
There's not an objective number for that. But if we assume there is, then you are simply guaranteeing that no rentals will exist, because landlords pay higher taxes than a resident mortgagor, and they have overhead.
Only if you ignore the appreciation on the investment asset (eg the house). That's most of the reason to rent out a house - for the future sale of the property. This would just mean landlords would need to buy the maintenance costs until they sell up.