In order to clarify things here;
There is consistency, then there are image qualities. Consistency is generally agreed to be a good thing, or even a necessity, but still it cannot drive over the image quality itself, and this is a very subjective matter. If the process does not yield results you like, what's the idea of keeping it consistent or doing it at all? OTOH, if the process produces the "look" you like, then small variations around this point won't necessarily kill this look instantly.
Typically, "replenishment" is a process used by large commercial laboratories due to economical and environmental reasons. By definition, a replenished process is less consistent, unless VERY carefully maintained. This requires investments, but the total sum is still much less than one-shot processing, given enough throughput (for example, more than 20 rolls a day).
Typical replenished process works like this: A replenisher solution is prepared. A separate tank solution is prepared -- this is the actual solution for the development. Usually the tank solution is prepared by taking replenisher solution and adding so called "starter" solution. This instantly drives the tank solution to the desired chemical balance, in a consistent way.
Then, film is processed in the tank solution. For every unit area of film, a certain amount of "replenisher" solution is added to the tank solution. The replenisher has an opposite chemical bias compared to the byproducts (most importantly, bromide and iodide) released from the film. This way, the chemical balance is kept constant. In addition, replenisher has higher concentration of development agents to make up for used (oxidized) development agents. And finally, one of the tasks of replenisher is just to simply drive away the same volume of used tank solution from the tank.
However, due to small differences in how much byproducts are generated (this depends on film, exposure and scene content), the process WILL inevitably slowly drift away. The large volume (typically in the range of 20-100 liters) of tank solution keeps the drift slow enough so that it can be monitored and corrected.
Drift is constantly monitored by running precision pre-exposed control strips (typically made by Kodak, Fuji etc.) through the process, for example one per 100 rolls of film. Using a precision densitometer, a small drift in density can be measured BEFORE it is noticeable by eye. Once the drift exceeds so called action limits, replenishment rates are adjusted to drive the process back to the middle of the curve.
This is considered as a minimum. In addition, chemical laboratory for performing chemical analysis (measuring actual levels of, for example, bromide from the tank solutions) can be used.
Now, running your own little replenished tank at home is a completely different beast. It WILL drift. It WILL be in order of 10x less consistent than typical one-shot processing. But I have to ask -- so what? If the consistency is good enough in practice, there might still be valid reasons to run an uncontrolled replenished process.
Now the REAL problem here is that even though XTOL can be used as a replenisher, there is no starter available. This only leaves two options; to formulate your own starter, or to "season" the bath in a really old way of just running film through. The latter is a bit inconsistent, laborious and expensive way.
It appears that there are pictorial reasons to use so called "replenished XTOL", because it is a different developer than the "normal" XTOL. Of course it is, it includes more restrainers than the normal XTOL. It will have different contrast, different curve shape and possibly different look in grain.
Many people have chosen the uncontrolled replenishment to achieve this. A much better way for a very-small volume user would be to formulate a starter -- a mixture (the most important ingredient being sodium or potassium bromide) that is ADDED to a fresh XTOL and which immediately makes the solution work just like the "good" seasoned XTOL. This way, it could be used one-shot for maximum consistency and very low volumes. There are free formulae for very XTOL-like developers. If one of those would be modified to add "starter", you could mix any amount you need when you need it from dry chemicals for extra low volumes, and get just the results you are getting from replenished tank with less hassle and more consistency.
But, if the replenished system works, why change it. Also, it can be very economical if you hit certain minimum volume. But as long as it is a replenished process, you can see problems like discussed in this thread. Typically, if the bath is not used for some time, the only really consistent and right thing to do is to toss it altogether and make a completely new bath. But this involves using a starter, anyway. If you don't have a starter, you are not being consistent anyway, so it's easier not to think about it too much. If it works in practice, then it works.