Is healthcare in Varanasi really this difficult?

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Honestly, I'm heartbroken and frustrated.

I'm currently in Varanasi and today I went to a children's hospital to get an appointment for a doctor. After reaching there, I was told that the hospital allows only 100 patients per day and that once the limit is reached, no more appointments will be given.

That got me thinking, what happens if the 101st patient is actually the one who is in the most critical condition?

This isn't even the first time I've experienced something like this. Around 20 days ago, something similar happened with my grandparent. Once the day's occupancy/appointments were full, we were basically told to come another day or wait until the doctor's next scheduled availability.

I understand that doctors have limited working hours and that a hospital can't realistically see an unlimited number of patients in one day. But shouldn't there at least be a proper system for triaging urgent and critical patients instead of simply saying, "Today's quota is full, come tomorrow"?

And this seems to happen in quite a few places in Varanasi.

What frustrates me is that healthcare is supposed to be one of those services where capacity should be planned around the demand. If a hospital is consistently getting more patients than it can handle, shouldn't there be additional doctors, extended OPD hours, or some proper system for managing the overflow?

I've lived in Mumbai for most of my life, and while Mumbai obviously has its own healthcare problems and overcrowding, I've generally found that if you can't get one appointment, there are usually other hospitals/doctors or another time slot available the same day.

Maybe I'm looking at this the wrong way, so I'm genuinely asking people from Varanasi:

Is this normal here?

Is the problem simply that there aren't enough doctors/hospitals, or is the healthcare system here poorly organised?

And more importantly, what is a person supposed to do when the hospital says "100 patients are already done, come another day", but the patient genuinely cannot wait another day?