Keep in mind there's official "COSC Certification" which by definition is going to cost more, and there's the COSC level of performance, which is often referred to, and which many watches achieve.... but without having the movements submitted, tested and certified.
Forgetting the Certification (piece of paper) there's no reason a watch in this price range cannot obtain reasonable performance in today's market.
While you do pretty much need Quartz (with some variants) to guarantee near-perfect performance, it's not at all uncommon to find watches well under 2K that will stay within a few seconds of zero, day in and day out.
But, since performance of mechanical watches is really an average of all positions, a lot of real world results will be skewed by how often they are worn, and how they are positioned when they are not.
Two owners of the exact same watch, with the exact same timing in each position can see different results simply based on how they wear their watch, for how long it rests each night and in what position.
If Adam is a desk worker and takes his watch off immediately upon returning home from work and stores it Dial Up while Zack is a UPS driver and only removes his when going to bed and stores it Crown Up they will almost certainly report back to us with very different results, and impressions of the movement's accuracy as well.
Myself, I store my watches on a winder, which not only keeps them fully wound (where mechanical watches deliver better accuracy) but this also randomly changes the resting position, thus helping to average out the positional differences.
This is why the timing apps that track daily rates aren't particularly useful for comparisons. They're handy and interesting to give you an idea of the results that you are receiving, but they are entirely meaningless in comparison to others.
Only testing in all 6 positions, using a decent timegrapher in a manner consistent with others is going to be in any way useful for collecting data and making comparisons. For example, testing at full wind -1 hour and again at -24 hours is a commonly used method for assessing overall performance. Purple Hayz has amassed a strong collection of data on this for us all.
As for myself, I have a number of watches ranging from $300 to $1,500 that are under 4 seconds a day. But, in addition to owning Rolex, Tudor and Omega, I also tend to buy used, gray market or out of favor watches that offer a lot of bang for the buck so you really can't put price range on performance of the movement.
In the end, there are plenty of people walking around with $5K plus mechanical watches that are more jewelry than they are great watches. Conversely, there are just as many (well, more probably) with $500 mechanical watches that aren't much in terms of jewelry, but that are really good at keeping time.