This is the flawed thinking that causes people to make the less financially-wise decision, if I'm understanding what you are saying correctly. Comparing $2000 in mortgage to a $2200 rent payment and saying that owning costs $2400 less per year misses so much of the picture.
Slap on a modest $2000 in property taxes you'll pay for for that property taxes, and you are already basically back to even. (I know you mentioned taxes in your specific case, but I include it in the list for the sake of accuracy for anyone else considering the math.)
Property tax is always rolled into the mortgage as an escrow. You're making up false numbers here. Renting a 3 or 4 BR single family usually means you're paying someone else's mortgage payments, including property taxes, plus some on the top to actually give them income.
Here's what you're missing: the money I've paid towards my mortgage principal can be recouped. And interest rates are so low that a mortgage on good credit is almost equal to inflation, so this is as close to a 'free loan' (0% APR purchases on cars notwithstanding) as you can get on an asset that you can reasonably expect to appreciate with inflation if you take care of it.
The money I pay in rent, however, is money flushed down the toilet. It's gone, forever.
DIY home improvement projects usually net positive cash value on resale. Yea, if you are going to hire a contractor for every little thing it gets expensive. Also gotta learn how to replace toilets, vanities, repair appliances, etc. Good thing it's the 21st century and YouTube exists. Most of these repairs take 1-2 hours and would run over $300 to have someone else do it. The larger projects can run thousands but taking a weekend to do arts and crafts yourself pays off and personally is rewarding.
Which is why it takes somewhere between 5-7 years to break even with all the other stuff you mentioned. There are several online calculators to help with this decision.