In the time that I have been doing this, I have bought probably around a dozen or so mounts.
Of them, I had one that was DoA, out of the box. It was a Celestron CGE with a dead declination motor. I gave the mount back to the dealer and they replaced it with one that worked. Other than that, every mount I've purchased worked correctly.
I think that some of the issue is the definition of "working correctly". In reading these forums over the years, I get the feeling that people expect far more from this gear than what it can actually do. Sometimes, there is this idea that you can take a new mount out of the box, put a scope on it, and start observing with goto's that put the object in the center of a high power eyepiece. Or put a scope and camera on it and do unguided deep sky imaging. That is simply not going to happen.
There are two critical aspects to success in this hobby:
First, you need realistic expectations of the gear.
In order to work correctly, a goto mount needs proper alignment. By far the most common error that I've seen in getting goto to work properly is aligning on the wrong stars. In order to properly align the mount, you will need to know the names of your alignment stars. In most cases, learning the names of a dozen or so bright stars in the sky is plenty to give you some good alignment stars. Also, you need to have your finder correctly aligned with the main scope. Otherwise, you might end up centering the right one in the finder, and a nearby - but different - star in the main scope. Also, there may be a specific technique required. For example, Celestron mounts want you to always complete the centering of stars using only the "up" and "right" buttons on the controller. This is important, as it ensures consistent handling of backlash. If you don't do this, you might end up with goto that mostly works, but not for all objects.
If you are planning to do some deep sky imaging, it's tempting to think that you can put your scope and camera on the mount, and start taking unguided exposures. That's simply not the way things work. With the vast majority of mounts, guiding is an absolute requirement (unless you only do very short exposures, like under 30 seconds - and even then you would need to be imaging a wide field). Even with the highest end mounts, you need some sort of sky modeling with tracking correction. This is because even if the mount is perfect, the sky itself is not perfect. Objects move at a different rate at the zenith than they do lower in the sky. Also, it takes only microscopic tracking errors to affect exposures. This means that mechanical flexure issues outside of the mount can, and do, affect the quality of the subs. Using a guide scope for guiding can deal with the sky issues, and some mount behaviors. But to address flexure, often times you need to use an OAG.
This is all perfectly normal, but isn't something that you will see printed in bold letters on the box.
Second, you should expect to invest in yourself as well as your gear.
An equatorial mount depends on an accurate polar alignment for tracking. Don't skimp on this. There is a continuous temptation to spend hundreds of dollars on polar alignment aids. But if you want to educate yourself, you'll learn that there are lots of ways to do polar alignment. For example, I polar align my mounts during the day, when the sun is high in the sky. I don't use any cameras, or polar scopes, etc. It just takes a reasonable understanding of the gear and the geometry of the sky.
Even with a goto mount, it is in your best interest to learn the sky. Sure, if everything works, you don't need that knowledge every night. But when things don't go as planned, it sure is nice to understand what the mount is actually doing, where it's actually pointing, etc.
For imaging, you really want to deeply understand all of the gear, as well as the sky, the weather, etc. There are whole books written on the things that you should know to get going with deep sky imaging.
If it helps, I like to use musical instruments as an analogy to astronomy gear. For example, you wouldn't expect to be able to pick up a guitar and play a song without first learning how to play a guitar. Yet for some reason, people (not referring to anyone specifically) expect that they should be able to plop down an astronomical mount, put a scope on it, and then have it perform as if the operator had years of experience.
In addition to the dozen or so mounts that I've owned, I have helped dozens more folks with their gear at star parties - many makes and models. The story is pretty much always the same. Someone goes to a vendor at the event for help. The vendor sends them my way. I give the gear a once over, correcting any setup problems, etc. I then align it and get it configured...and it works fine. Except in cases of mounts that are missing parts, or are physically damaged, I've only encountered one mount that I couldn't get to work right. It was a Celestron AVX. The owner had made significant electrical modifications to it. When we powered it up and tried to align it, it gave me a mild shock any time I touched it. I spent a few minutes with it, before deciding that the best course of action would be to reverse all the electrical mods and return it completely to stock.
So in my experience, the overwhelming majority of mounts work just like they are supposed to (even if the owner wants more out of them than they are designed for). There are certainly some mounts that don't work well (or at all) out of the box - but they are actually pretty rare, and either the vendor or manufacturer needs to get involved. In most cases, what's needed is some education for the owners. Even then, I have met a few people who just aren't interested in putting in the work to learn the techniques - and follow them with an appropriate attention to detail. They want it to work they way that they have pictured in their head, and not necessarily the way that it's actually supposed to work.
I will say this, though:
You do tend to get what you pay for. An expensive mount tends to be better at everything that a lower cost mount. The quality of construction is higher. They are physically more durable and resistant to damage. The tolerances are tighter. They perform better and more consistently. They last longer.
But you still need to understand how they work and their limitations.