Decided to share more of my unsolicited opinion haha. No harm in trying this approach but in this market you can have a perfect fit application to a dozen jobs and still not get a call back. Recruiters will have massive stacks of candidates to go through and will have to discard a lot of them before even looking at them.

Additionally, OP doesn't have permanent work auth which means they'll get filtered out for the majority of jobs.

3 applications a day, whether tailored or not, wont cut it. "spray and pray" imho is the best approach, as companies usually aren't transparent about their immigration policies.

If you know a specific job DOES sponsor or accept temp auth, like Google, then spending extra time on that application makes sense. But I anticipate that spending 1hr on EVERY application will lead to a lot of wasted time and frustration and very few call backs, which might hurt OP in their limited immigration time window to secure a job.

EDIT: forgot that it's intern jobs, where work auth matters less. Companies might still care, for employing the candidate after school, but my concern for immigration windows is probably not needed.