That's like saying you shouldn't have elections because totalitarian dictators can abuse them. If your boss's plan is to make you feel bad, it doesn't matter what management technique they use.
As a boss the problem is employees take up so much time. Each employee really needs at least 30 minutes of your attention per day averaged over the month (mostly just chit chat, but also mentoring and feedback) [1]. Once you have more than a couple of people to manage there goes your whole day.
1. Yes some people are fine with less, but this is the average amount of time people need. Putting in less just results in a build up of management debt that will come back and bite you in the butt.
Having had from 3 to 14 direct reports the ideal is probably around 7. Too few results is too much attention ("hey boss I have a job to do") while 14 results in total burn out and neglect ("we haven't spoke in weeks - what is your name again").
The latter statement proves the former. A good manager prioritizes management over work that an individual contributor might do. If that doesn't suit a person, they're likely not fit for management.
Tell that to Gartner Group: according to my management they recommend an average of 10 direct reports. They also recommend you don't have "technical managers" just pure managers without technical delivery goals; all that is strictly delegated to individual contributors.
If your management is buying "advise" from the Gartner Group, that is a "bad management smell" IMHO. My advise is to work on your escape plan.
Every time I read or hear Gartner Group "information" piece on a subject that I am competent to judge the value and accuracy of the information, it is at best useless fluff, typically is mostly wrong, and commonly totally wrong.
"An average of 10 reports" goes against the commonly accepted magical number[1] of 7 +/-2. I suppose if the "pure" managers are only pushing paper (unable to judge technical merit), they can support more direct reports. That structure sounds like a recipe for perpetual technical problems.
What you quote sounds like classic matrix management[2] which results in two bosses, one controlling your HR side and one controlling your technical side. That does not work well in my experience because the two managers have very conflicting goals and neither of the goals are in in alignment with your goals. In the ensuing fight, the HR manager always wins because he controls your pay and assignments... and usually is the manager whose goals are least aligned with your goals.[3]
[3] 24 years 9 months in a large corporation with matrix management. It was OK until the Ginormous Enterprise bought the division and sucked all the fun (technical work) out of it.
They are utterly and completely useless.
You should speak with your boss continuously, regardless of the 1 on 1s.
Maybe it's a coincidence but with all the worst bosses that I had we had 1 on 1s.
It's just a way to hide their incompetence in my opinion.
The problem with being continuously available is that it leads to "squeakiest wheel" syndrome where the loudest complainers get all the attention. Meanwhile, the quietly productive people quit because their frustrations aren't heard.
In my experience 1 on 1s are nice because it allows me and my boss to speak in private consistently. When we are both in cubicles it's hard for me to have candid conversations if I know everyone is listening. It probably depends on the person but I have always really liked one on one meetings.
It also establishes a pattern so that other employees don't automatically assume that seeing you and the boss in a meeting room means that you're having a candid conversation.
Managers need to be available when things happen. I mean, they have other meetings, but during the day they should be able to give or receive "immediate" feedback; don't wait until the scheduled weekly (if you're that lucky) one-on-ones. However, if everybody is busy, and there's no immediate need to walk into each other's (virtual) office, it's good to have the scheduled interactions, to make sure you're still aligned as well as still pleasantly interacting as humans. (If the latter wasn't the case in the first place, maybe... wrong job.)
1 on 1s are not for feedback on day to day stuff. They are supposed to cover the more meta aspects not related directly to delivering on a daily basis. If your boss is using 1 on 1s to cover operational stuff they're wasting the opportunity to help improve the team wellbeing and progress.
I don't think we really had a disagreement, here. Just keep in mind that one-on-ones vastly differ between companies and managers, among other things in frequency.
In my situation, my boss is one of the 10 other people in the same office (when he isn't in meetings). All of us ask each other quick questions but try not to hold longer discussions there, because it disturbs everybody else. So more than that becomes a "one on one" in the discussion room. Nothing scheduled.
You need to use them for positive feedback as well as negative, and general chats about progress and ideas.