Yes, everything will go up. That includes the cost of the asset itself and the cost of borrowing money (credit). These are the biggest chunks and the ones you can keep stable, effectively detaching them from inflation (it’s tricky though).
Anyway, all these costs are passed on to the renter. Renting therefor is more expensive than owning in the long run. It’s simple: if it isn’t lucrative it wouldn’t be down. To be lucrative the additional costs need to be passed on, regardless of which type of cost this is.
Buying a home doesn't improve cash flow on the income side, but on the cost side of the equation, if done right.