OSU vs Private School (int'l applicant)

I’m applying to a handful of top tier private schools in the US but I’m wondering whether or not it’s worth it to apply to any public schools. As an international student I would be able to get max $15,700 in scholarships (from what I’ve read) from Ohio State whereas at a private school I could receive financial aid that would offset my total cost by much more.

I believe I have the grades and ECs to get into OSU but if I don’t have the money should I just try for private schools and if I don’t get in stay in my country (Canada). Basically what I’m asking is whether or not it’s worth it for the massive amount of money I would have to pay to attend when I have other arguably ‘better’ options that are just harder to get into…

currently in grade 11
PSAT: 1380
Projected ACT (via their own prep program): 32
Unweighted GPA: 95/100

Extra curriculars:
Varsity tennis (9-11)
Varsity tennis captain (11)

Club Tennis (10-12)
Winner of a few notable tournaments in my province
Provincial Champion Winner of the high-performance league (as a club)

Competitive Robotics (9-12)
Captain (10,11,12)

Student Council (9-11 +12)
Executive Member and running for president for senior year

Queer Straight Alliance (11-12)
Club Leader (12)

School Newspaper
Advice Columnist (10)

I would apply to some public universities because they are much cheaper. Than the 71k you would be spending at top tier private university. I had very similar stats and I didn’t receive much merit aid. University of Notre Dame gave me 41K off, so I would apply there. I got into the morrill scholars program at OSU, and they gave me full tuition.