The key is to treat people as responsible adult professionals with the best intentions. This way communication will happen organically and proactively. For organic proactive communication async channels are ideal. When you bump into a problem you need help with you message someone you think can help. They will eventually see your message and find the time to reply (seeing and replying won't always happen at the same time). This type of communication is extremely efficient and sustainable. Sync communication also has its benefits and they're trivial to set up using async comms if/when the need arises. This does not mean that recurring synchronous communications aka. standups are bad per se but their value is highly context dependent and oftentimes they are not the best solution.
On the other hand if you treat people as irresponsible children that needs constant supervision then, in my humble opinion, nothing will save you on the long run and implementing mandatory protocols like a daily standup are just surface treatments.
The whole Agile (tm) is a surface treatment for having a grasp on complexity. It's more of a ritual thing than an exact science.
The introvert developers are sometimes so introvert and protective that they deliver at the last possible moment stuff that doesn't follow any conventions set by the team and in some cases makes stuff explode after merging.
I would rather have them forced to give me an update and subsequently a pretext to get a peek at their work under the guise of helping than have them fail the whole team. Eventually they shed their impostor syndrome, or at least I hope they do.
Personally, I've been on both sides of this pattern and I would rather still have standups.
As for supervision, I've seen teams selling bullshit with glitter on standups if there were transitional people or stakeholders. Then it's nothing more than the usual status update dance.
Sometimes I run into a really tough problem, and good team members don't need to have a system to force this behavior. In fact, I'd say it's within the prerogative of a developer to withhold problems they believe they can work through so that other cooks don't jump in to crowd the kitchen, and so that managers don't make a counterproductive decision to dislodge a perceived roadblock.
As you say, some programmers are proud and don't want to seek out help. Does this reflect in their work? If it doesn't, then who cares? And if it does, then management should resolve the issue by whatever means necessary. Trying to force "I'm facing a tough bug" out of people is not the way. Creating a culture that fosters collaboration, on the other hand, seems more effective in getting people to seek genuine help.
Just make standups about the people. Hire good engineers or engineers with potential and invest in them, and allow their team to function naturally. Remove the goal-orientation from standups and just give teams 10 to 15 minutes out of the day to just shoot the shit. Having to make it about going person-by-person and saying "Yesterday, I did X...", "Today, I'm doing Y...", or "I ran into some issues with X-thing", is really just like being back in elementary school where the teacher picks on students. I know some people don't seem to feel this way, but I'm really not that interested in going back to the 3rd grade.