What do you do when talking leads to them saying "I understand, next time I'll either get it done faster, or let you know when I realize it's gonna slip" but then what actually happens is that it slips without them giving you any updates again after all? Repeatedly? Talking doesn't build trust when the actions don't match the talk.
If there's a persistent lack of communication when it should've been known that a deadline is not going to be met or is at least going to be close, set-up a PIP where you lay down a checklist to follow at the start/end of the day of behaviors you expect regarding communication.
If that doesn't help, then yes, firing is the correct response, not permanent micromanagement.
This is all under the generous assumption that your deadlines are actually very important in the business and plans will have to be shifted if they're not met because of a harsh business reality. Otherwise it's your fault for allowing the cost of deadlines to be incurred in a team where all they will do is hinder morale, add bureaucracy and reduce productivity.
As far as most dev teams are concerned, timelines are less important for the business than they are to each other.
People don't like it when they are constantly waiting on person X to finish their part of the work. (That's a good way to know you've really dropped the ball as manager: the other team members start asking YOU what's going on with the other person.)
You say that you want X. X has to be reasonably achievable. You don't tell them how to do X, though.
That introduces another set of problems. You have to do X within Y.
Suddenly you know more of Y than X. So then you turn towards Z and you have to do XY within Z, but Y is more important than X.
Another possibility is that the environment is one in which it’s not okay to admit that schedules are slipping, despite the manager’s insistence to the contrary.
There are many more possibilities of course. Does the employee have any insights into why they failed to take the action they promised?
If a designer makes an unresponsive site, the manager can just say "hey do a responsive design tutorial". But if the designer gets all kinds of patterns or structures or the company design language just wrong, it's very hard to discuss that without making the designer feel like you're micromanaging them.
All of your examples can be handled with good communication. If a designer makes an unresponsive site but the site should be responsive, then the communication failed and the requirements were wrong.
If you're a manager or a leader then, ultimately, you are responsible for the failures you presided over. You can't sit back and observe the chaos.
Sometimes you can have a Frank discussion about it, or regular ‘adult’ type discussion, and there is something that can be done that fixes it, and it can be fixed. That is not always the case. Sometimes the person is fundamentally incapable of doing the work (rare), or in a place they can’t care about or don’t want to do it - but won’t or can’t acknowledge it.
Re:accountability - there are many different definitions one can use for what this really means. The clearest I am familiar with is ‘if you can’t or won’t do the job to standard, and there is no special circumstance like a leave that should be applied, you don’t have that job anymore’.
That is easier said than done in many business environments.
I’ve worked in places where someone literally not doing any useful work was going on a year+ of dragging on with the team, constantly changing reasons for why they couldn’t do the job, and killing the teams morale. Literally 4 layers of management involved in HR processes trying to drive this to a useful conclusion, but new buttons being pushed every month by the employee and a highly risk adverse HR/Corp culture meant the situation couldn’t be resolved. All this on top of 6 months of coaching and attempting to help this individual be a productive member of the team.
These environments all require micromanagement of low performers as part of the performance management process - it’s the way things have to be to get the documentation and proof of coaching for CYA.
Accountability isn't easier said than done; it exists everywhere, but you choose how to apply it and when and you use your bias to decide how hard to apply the discipline.
If you feel you need to micromanage someone, then you've lost your leadership too.
If you, as a leader, will get fired for holding someone accountable to the job (and firing them) and stopping a toxic environment from happening on the team, what then? What if the reason for that is some meta PR corporate reason that makes sense for corporate maybe but not for you and your team?
What if your job includes not causing those larger corporate issues and following the rules of the larger org?
It’s a failure of a large organization, and part of that failure is often making sure there is no one to actually hold accountable in a real way. It sucks. It happens.
Did you take the micromanaging approach because you didn't open a channel for feedback between you and the team?
Micromanagement is one thing: a lack of trust. You micromanage because you don't trust, or maybe they don't trust either. So, what do you do to build up trust? You talk.
Note that this is different to accountability. You can hold people to account without micromanaging them.