Here are a couple of questions.

Assuming that a tank is stocked correctly...

If the point of filtration is to create water parameters that are perfect, zero ammonia, zero nitrite, nitrate below 20 etc, and if these results are achieved by using a filter system which turns over less than 10 x the water volume held in the tank per hour, what exactly is the problem?

Just wondering.

When and if your fish reach full size you well need the 10 x turnover to keep up. Goldfish are messy. My 75 gallon has 1050 gph. And I only have 4 in there at this time. However hubby brought home a new one last week that well be in there in a month. So that well be 5 goldfish and 4 BN I need all the filteration I can get.

The more you can achieve the better off I think goldfish are cause of the mess.

Yes you can temporally get away with less if you do larger and more often water changes. But in the long run you want the 10x plus for your goldies.

I wonder if anyone will post that they have less than 10 x (with full grown fish) and perfect water conditions......

Unlikely.
The larger a fish grows, the greater its ammonia output. Most people with large fish start to find that their nitrate levels become increasingly hard to manage and need to upgrade their tank size and filtration levels.
It's sometimes possible to keep up with several water changes per week, but the x10 rule has really been established through hard earned experience.

i have 20 x

Aside from the nitrogen cycle, large filters also provide other valuable services for the tank: removing unsightly detritus (hence preventing it from rotting), creating aeration (more = better, especially in the high heat of summer), and preventing water from stagnating. Even if you had a perfect nitrogen balance in a tank with less than 10x turnover, those other issues would still plague you and force you to do extra water changes.

Just my

The whole system of a tank is a balance of all the factors that go into createing your ideal fish environment. You can "get by" with less than 10 times filtration if you adjust other parameters. Green water typically uses far less water turnover - and does not use the nitrogen cycle. Fitration done with Zeolite does not need 10 times - but benefits from it or more. Continuous water exchange does not require 10 times.

The 10 times rule is something that, just as the "one fish per 10 gallon" rule, is a "rule of thumb". It is not exact! You CAN put more fish than one per 10, but not one in 10. A 70 gallon tank can hold more than 7, but a 20 gallon tank would be hard pressed to hold 2. A tall 50 gallon hex tank probably needs more filtration than 500 gph, but a longer 50 gallon tank would be fine with two or more filters that pumped 500gph......

If you have less that the 10X, you may find that the water is "murkier"..... it may or may not be crystal clear. If you change out the water, have a nice carpet of green algae, rinse your cartridges/sponges between changes, feed sparingly, have no gravel substrate, feed gel or live food instead of pellets, etc. you can effect the wataer parameters greatly. Adjustments of many of these factors can all effect the water parameters in a tank/pond.

Actually, I do have fully stocked tanks with "less than" filtration, just as I have fully stocked tanks with 20X and more. My average tank that is run on the nitrogen cycle runs somewhere on about 16X. So much depends on a whole host of other factors in the methods, tools, and equipment you use in the individual system.

A good rule of thumb is 10 X turnover, 10 gallons per fish. A realistic rule is.... let your water tests guide you in how you keep a tank. The filteration may need to be more or less, the water changes may need to be more frequent or of greater volume or both, the feeding may need to be cut back, the cartridges may need to be rinsed, the substrate may need to be limited, etc.

Keep in mind, as your cartridges/sponges/media fills, as the filter ages, as the tubes pick up alage and other "grunge", the filter will be pumping FAR less gph than it is rated as doing. A 400gph of an average 1 year old Emperor 400, if measured emperically, is more like 320gph....... (but for that matter the average 10 gallon tank holds 9 gallons!)

I agree with thoughts of joy... filters also create circulation and aeration. Goldies need lots of oxygen. If they're forced to get oxygen by surface breathing, then you're creating a whole other set of problems via sbd....