Especially from my many years of Tai Chi Chuan training and practice I've see many with bad form and posture, I see this in the Yoga studio. A good teacher will come along and correct your form and posture, a good teacher moves around the class instructing, also give a demo to show if anyone is a little confused.
The fact that you're seeing "bad form and posture" even in yoga studios is evidence that attending in-person classes is no panacea. Not all teachers (or even all studios) provide hands-on adjustments these days. There are huge liability issues with doing so, and a lot of students, frankly, don't want to be touched. Certainly the teacher should be observing their students and at least providing verbal adjustments where necessary. But there flat out is not enough time in a public class to help everyone adequately. Especially in an "all-levels" class--which, for financial reasons, is what pretty much all public classes are these days. Also: an in-person class can be an overwhelming experience for someone who is brand new to the practice. There is a lot to learn, and students can certainly miss things in trying to take everything in.
I would posit that there are many reasons you are seeing in the yoga studio what you refer to as "bad form and posture":
1. There is no one "right way" to perform a yoga asana. Certainly there are standards. But these can vary from one yoga lineage to another and can also vary between yoga and other movement disciplines. Sometimes the student is simply doing the pose the way they learned it because that's what they know/are comfortable with. If they've conditioned their body to be able to do the pose that way, they're probably fine.
2. Every body is different, and the same pose looks different in different bodies. Some students have injuries or other mobility issues which prevent them from executing a pose as cued. Others may deliberately take a pose farther than we would normally cue as "safe" in a public class because they need that more extreme movement for some other discipline they practice and so are training their body to be able to handle that standard. Others still may simply be more comfortable in one variation over another. There are many modifications for pretty much every pose and many reasons for using one.
3. Sometimes people's poses are sloppy because they're tired. Sure in an ideal world we'd all be 100% present in every practice and push through our tiredness to execute every asana "perfectly". But we don't live in an ideal world. I've taught a lot of evening yoga classes in fitness clubs where my class was the last class of the day. Sometimes students came to my class precisely
because they were tired and they needed a break from the stresses of their day to help them wind down before bed. If such a student is half-arsing their active postures because they're just using them to loosen up for the restorative work at the end of class, I'm not going to worry about it.
4. Sometimes the student has not yet learned the goal/intention of the pose, as you suggest. Maybe in this studio class the instructor will give a cue that clicks for them and they'll achieve understanding. Maybe the pose won't truly click for them until the next class they take, or the class after that, or the one after that. Maybe it will never click for them. It's all good. There are many benefits to a yoga practice beyond simply executing the asanas "perfectly". If, however, one has a goal to learn to perform yoga asanas to a specific standard, I will again argue that a good instructional video can in fact be more beneficial than a live, in-studio, yoga class--even one led by the very best of yoga teachers. A video can be paused, rewound, viewed again. With a video, every student can take exactly as much time as they need to learn every pose. And if they're not able to feel whether or not they're performing the pose as desired they can always video themselves and take a look at what they're doing.
Certainly in-person classes are great too! The energy of the room, the community with the other students, the opportunity to receive real-time feedback from a knowledgeable instructor, and the opportunity to ask them direct questions. All important benefits of the in-person class. But there are many reasons (geography, scheduling, finances, infection risk, fear) why in-person classes are not an option for everyone. Fear is a big one. Many people are intimidated by the prospect of walking into a yoga class for the first time. If someone wants to try public classes but is nervous about beginning, instructional videos are a great option for gaining some familiarity with yoga concepts and enabling them to feel prepared to venture into the yoga studio.