If you know that you have a scheduled meeting coming up, and then you scheduled your "deep work" to run over the top of it, that's not great time management on your behalf. It's also potentially a symptom of inefficient scheduling, since it should be possible to schedule meetings (especially 1on1s) at a time of day that is least disruptive for the participants.
I do know how easy it is to get in the zone as a developer, and subsequently feel frustrated that a useless meeting just popped up in the middle of your flow, but that's not a good reason to write off 1on1s entirely. Worst case your flow will be interrupted once a week. Two if your team has a weekly retrospective as well. If two interruptions per week is significantly damaging your productivity, something is wrong.
Personally, I am not a fan of meetings in general, and I do consider many of them to be useless. But 1on1s and retrospectives are the two that I mandate in the teams that I lead - one is for the health of my reports, and the other is for the health of the team. All other meetings can and should be optional. If someone is feeling snowed under by all the other meetings, then it's exactly during the 1on1 or retro when those feelings can be shared. If you don't have those meetings, then you're relying on everyone on the team to always speak up whenever they need help, and while that might work for certain, very assertive and/or self-centered employees, it doesn't work for everyone. For that reason I think it's important to schedule these times in deliberately to give people the opportunity to express themselves.
When there isn't a culture of open communication - which is established through regular meetings of this sort - many employees find it difficult to be honest about their challenges and difficulties (on the negative side) or goals and aspirations (on the positive side). In either case I believe it improves productivity and retention to give employees dedicated space to talk about that stuff.
If I have a standup at 10am every day, this guarantees that I'm not going to ever get anything substantial done before 10am. A 3pm weekly meeting can mostly destroy my ability to get in to deep work for that afternoon.
I don't "schedule" deep work, it is a thing that happens as a combination of what needs to be done, the time available, minor tasks, and interruptions.
Daily and weekly meetings significantly reduce the surface area available for these things to happen, and often serve as a source of boredom and frustration, being in a room with people who obviously don't have anything to say, saying words because they're supposed to.
If you feel that all of these meetings are significantly impacting your ability to deliver your work on-time, and your experience was shared by everyone on your team, that should have come out in a retrospective, and your team should have decided to scratch those useless meetings. If your team never had a space where you could discuss and act on things that you find to be disruptive, then that's exactly the reason why your manager needs to make sure you have that space. Or, if you did have that space, and you did share your feelings, and it turned out that you were unique and everyone else finds these regular meetings useful, then it might be worth thinking about why it is that you don't get anything out of these meetings but other people do. Then it might be worth speaking with your manager to see if the team - or the position - is a good fit for you.
The whole point of 1on1s and retrospectives is to optimize your work. If you literally only have these two meetings per week and you still find that unreasonably disruptive, then you could discuss dropping them to once a fortnight. If you still find those two meetings per fortnight unreasonably disruptive, and you really get absolutely zero benefit from them whatsoever, perhaps you should be working as an independent contractor and not a salaried employeee with a team of colleagues and a manager.
I do understand where you're coming from. I have had several direct reports who never had anything at all to say in their 1on1s, who had no interest in setting goals, no interest in advancing in the company, no interest in improving their workflow, who honestly just wanted to sit down, do the work, get paid, go home. That's fine, and it's useful to have some people on the team who want to work that way, but they really are a minority of people I have worked with in "normal" company environments. To be frank, I would prefer to work that way myself, but that's not really how most companies operate, because most companies are geared for growth, so it's not enough to just stay at the same level of productivity forever. The goal for most companies is to continuously improve and increase their output, forever. This is why most companies see value in having these meetings, because they are a way to focus employees on becoming ever more productive.
I would recommend you read Deep Work by Newport. It's not parent commenter's inefficient scheduling or his opinion; even just knowing you have a stop coming up interrupts the deep work process. Every meeting is incredibly disruptive on both sides of it.
I do know how easy it is to get in the zone as a developer, and subsequently feel frustrated that a useless meeting just popped up in the middle of your flow, but that's not a good reason to write off 1on1s entirely. Worst case your flow will be interrupted once a week. Two if your team has a weekly retrospective as well. If two interruptions per week is significantly damaging your productivity, something is wrong.
Personally, I am not a fan of meetings in general, and I do consider many of them to be useless. But 1on1s and retrospectives are the two that I mandate in the teams that I lead - one is for the health of my reports, and the other is for the health of the team. All other meetings can and should be optional. If someone is feeling snowed under by all the other meetings, then it's exactly during the 1on1 or retro when those feelings can be shared. If you don't have those meetings, then you're relying on everyone on the team to always speak up whenever they need help, and while that might work for certain, very assertive and/or self-centered employees, it doesn't work for everyone. For that reason I think it's important to schedule these times in deliberately to give people the opportunity to express themselves.
When there isn't a culture of open communication - which is established through regular meetings of this sort - many employees find it difficult to be honest about their challenges and difficulties (on the negative side) or goals and aspirations (on the positive side). In either case I believe it improves productivity and retention to give employees dedicated space to talk about that stuff.