What you're talking about does exist, but it is specialized. For example, UTA (Utah Transit Authority) has both UTA On Demand - a "microtransit" service that's basically an Uber run by the bus company - as well as Flex buses that will deviate on request for a slightly higher fare (although you do have to set it up in advance). UTA uses these services for two specific niches of transit riders:
1. People who live in transit-poor suburbs
2. People with physical disabilities
To be fair, these have significant overlap. The common factor being "demand that can't be aggregated to a fixed bus route".
Once you have enough demand to have a fixed bus route, however, the most important thing is frequency. Schedule anxiety is the worst part of taking any public transit system. I find that if a bus or train comes every 15 minutes, I stop checking the schedule. Additionally, once you start scheduling frequent buses, then transfer times go down, which makes the bus network dramatically more usable.
Think about it this way: if you need to take a trip that involves a transfer between two buses, and the buses come hourly, you have an average transfer time of... 30 minutes, where you won't be doing anything to progress towards your destination. Your transit operator can futz with scheduling to try and make that transfer tighter, but buses infamously have to share infrastructure with private cars, which means they'll never actually come on time. The worst case scenario being you schedule tight transfers on an infrequent bus, then the first bus gets delayed enough to turn that tight transfer into an hour long wait[0].
Alternatively, you can just run more buses, and so long as they all make progress in the road grid you get tight transfers naturally. Miss your transfer? Oh no... anyway, here's the next bus.
On the other hand, if you're seeing three empty buses pull up to the same stop all at once, that sounds like you have bunching, which is the most catastrophic failure mode of any transit system. What happened is that your transit agency scheduled frequent buses at reasonable times, but some blockage along the route - traffic, construction, etc - delayed a bus long enough to arrive alongside the next bus in the sequence. The front bus will be nearly full and the next buses on will be almost empty. And as the day continues this can continue delaying buses until you have destroyed almost all the capacity and frequency in the system unless they take emergency action to pull buses out of the system and reinsert them at different parts of the route.
The way you prevent this is to give the bus dedicated lanes. The whole BRT (Bus Rapid Transit) concept involves moving bus stops to the center of streets, having offboard fare payment[1], level boarding, digital signage, signal priority at stoplights, and so on. Some of this is just to make BRT feel more "train-like", but a lot of it also lets buses maintain a tight schedule and not bunch up.
[0] I am aware of some bus systems where the bus drivers will actively radio one another to request a delay specifically so that riders don't miss their transfers. AFAIK, Suffolk Transit will do that, but only if the two buses are on the same part of the network, since ST is actually four bus companies wearing a trenchcoat.
[1] When bus drivers are responsible for fare collection, riders have to all enter from the front and all other doors on the bus are exit only. Which increases dwell time (the amount of time you spend at each stop). In fact, this is why Zohran Mamdani wants to make NYC buses free - specifically to speed them up.
Also, while I'm talking about bus boarding, I have rode buses in Japan that had people paying with IC cards enter from the rear, or worse, enter from the front and then tap your IC card at the back exit while the bus driver is trying to explain this to you in incomprehensibly mumbly Japanese.