First of all, the goal would be to pay less rent to increase cash flow. Second of all, you can get out of a rental agreement and move to a cheaper location a lot easier than getting out of a mortgage.
While a good goal it is seldom I have seen a rental that was less than what a mtg is. Neighbors moved in across from us at the same time we bought same house basically, our mtg was $1765 their rent was $2000 when we left 10 years later they were paying $3000.
In the last two years we were paying rent at a third world apt complex it felt like and rent was $2200 nice building but difficult tenants. We bought this house, mtg is $1850. and a very nice place.
Certainly there are rentals cheaper than $1850 but I doubt they are in good shape, you are still not saving anything or making equity, just giving your money away.