In the first year of a 30y mortgage, yes interest is a big component... But even in year 5 or especially in year 10+ interest is much smaller and the principal impact greater. The long term impacts of ownership are the benefit, of course a large purchase will not stack up against renting in the short term!
Yes, unless I missed something, the analysis doesn't account for the decrease in interest costs over time. Still an interesting piece, just would be a fairer comparison.
The std deduction is fairly large now. You have a tough time getting past it for most people. There is also a cap on how much you can deduct. When I had a mortgage I calculated that about half way through the loan I would no longer be able to deduct the interest because the std one was bigger. One guy I worked with said this 'i love using the standard deduction it means I am not paying money to get my money back I am getting a lower tax rate'.