Yeah, it wouldn't even make sense for renting to be cheaper than buying. Most renting is from for-profit landlords. Obviously they have a mortgage, too. They're obviously going to try to make a profit. Plus mortgage is only part of the cost of owning. There's also property taxes and maintenance, which renting includes in the rent price.
The problems are mostly that there's not enough supply (most commonly due to bad zoning), homeowners oppose anything that could help (cause that would reduce the value of the home they already own), and that most of these landlords are for-profit. Being for profit means they aren't just going to charge more, but they also have a vested interest in making sure it's more expensive and less tenant friendly.