Taxes and maintenance wouldn't be included in the mortgage. A new roof is expensive, so are HVACs, floors, etc. These things will need to be replaced. A rule of thumb is to budget 1% to 4% of the total house value per year. For a 400k house that could be up to $16k extra per year, or $1333 more per month than your mortgage. Those costs for maintenance and taxes don't go towards paying down your principal so they aren't directly gaining equity. With the rent and invest option, the investing is the counter to equity. When you sell your house you usually pay a realtor commission. There are a lot of factors to include when seeing if rent & invest is better than mortgage & buy.
That being said, I prefer to buy. I don't plan on moving anytime soon.
Even as a tool it lacks predictability / reproducability. If I give instructions to download a paint program, start a new canvas of 1920x1080 and use the gradient tool to go from red to green, you're going to get the same result every time. If I instead told a class of students to ask an AI to generate a red to green gradient on a 1920x1080 canvas, the results would not be consistent.
I use AI, but it is a tool with flaws.