1:1 meetings are extremely useful. Weekly is excessive, though and I am not sure how a manager could find the time for so many meetings. Schedule 30 minutes once a month and keep those meetings informal.
All but one of my managers had their own bars set to quarterly meetings and all failed to deliver, so yearly one-on-ones it was, which is just silly. The one who tried to have monthly meetings ended up finding time for bi-monthly meetings. I appreciated the frequency, but they were completely pointless because he would ignore everything that he promised and forget about it until the next meeting, even though he himself took records of what he promised to improve in the relevant IT system. In the end he usually blamed me for not getting back to him, even though I would complain about the same things for months and he always promised to fix them. I don't think quantity matters that much, if your manager is capable and your work environment halfway decent you get away with a lot fewer meetings (especially if you have ad hoc ones when they are needed and you receive regular feedback when you need it - which doesn't have to and imo shouldn't be contained to booked meetings) , and if they are not those meetings probably are a waste of time and energy. Quality is more important than quantity.
No process can make up for a bad manager. But 1:1 meetings are very useful for decent managers and, IMHO, monthly is a good balance: not too frequent but frequent enough to be able to discuss ongoing topics and issues. Note that these are not for feedback on performance but rather for informal discussions to coach and get a feel of issues and generally to build rapport and trust.