You have to spend money on interest to have a portion of that reduced in taxes. It's not a penalty.
It's not a 'tax penalty'. You're keeping more of your money by not paying interest, and pay normal taxes on those. It's not a penalty.
That's really bizarre (although unfortunately, common) thinking.
There's an incentive for having a home mortgage under certain conditions only, and you do not owe anyone additional money if you have no outstanding mortgages on properties.
The same is not true for the ACA. You are fined for not owning something - e.g. if your net worth was $0, you could go into the negative for not having insurance.
If you don't own a mortgage, you cannot be fined into the negative.
There is no difference between a tax penalty and a tax incentive (more precisely, a tax incentive is exactly identical to a general tax cut plus a tax penalty for everyone who doesn't qualify for the incentive, and a tax penalty is equivalent to a general tax increase plus a tax incentive for everyone not subject to the penalty; so, except as concerns the general level of taxation, penalties are exactly the same as incentives.)
> If you don't own a mortgage, you cannot be fined into the negative
Since having a mortgage or not can make the difference between owing net income taxes or not, if you have $0 net worth before a particular year's taxes are considered, you absolutely can be "fined into the negative" for not paying interest on a mortgage (lenders, not borrowers, own mortgages.)
There is a tax penalty for not having a home mortgage, so it's mandatory in exactly the same sense that health insurance under the ACA is.