What do you expect a reviewers system to be

I'll expand a bit on your question to talk not only about their systems but also their credentials.

I expect what nobody seems to do:

1. Maintain an inventory of a good solid state amp and a good tube amp of 100 watts or more to give every speaker a good chance (many speakers prefer one over the other), and to let us know how it works with our preferred amp type.

2. Have their own 2 reference speakers so that they catch themselves from falling into love with one particular stylized sound.

3. Check their reference speakers against headphones too, for a third baseline that is also portable and room independent.

4. Listen with their ears and not try to play engineer/designer/physicist (unless they are one) to figure out what it might sound like or why it sounds the way it does - this only gives them prejudice which is almost always unfounded.

5. Not review equipment that is way more expensive than their own product of that type. They need a reference in the same ballpark, and to have experience with others in the same ballpark, as what they are reviewing.

The above would be for starters. There are many other issues of experience, honesty, lack of deep friendships with particular companies, favoritism due to advertisers, familiarity with real music (they all claim it but most don't go to many concerts, many don't go at all), and other things I could list, but we are not going to get even what I list above. Unfortunately, this is a cottage industry at the high end, and the reviewers are just as home brew as most of the designs, with little accountability (actually, none).

In the old days, the reviewers at ABS and Stereophile used to list the records and equipment used to evaluate the equipment, and point out specific areas of the music where the equipment acted in a certain manner different from their reference. that way, you could play the same album and see if you heard the same thing. I thought that was a good way of transfering the reviewers experience to something I could recreate in my home. they seem to have gotten away from that.
ABS especially would have a number of reviewers review the same piece of equipment and have their counterpoint to the main reviewer. I found that to be useful also.
I suppose these days of instant gratification require a quick turnover of equipment to ensure that the latest and greatest gets reviewed and printed ASAP. Perhaps quantity over quality. When ABS and Stereophile were underground mags with fluctuating publishing schedules, they could take their time until they had enough to fill a magazine. Now, with monthly schedules they print what they have to fill the space, and not a lot of followup. But, it must be a more successful business model as the old journal style almost went under. I preferred that old, small book style. Seemed a little more important than the magazine format.
I dont have a problem with the reviewer publishing what the manufacturer states is their theory for the product, so long as we know thats what it is, manufacturer explanation. We can take it or leave it. I dont like when a reviewer just copies the manufacturers brochure to pass off as his own explanation of the science involved. Just tell me what it sounds like, and if it works properly with no quirks. If it takes a month to warm up before it sounds good, say so, and I will pass. If it only works with certain cables, to me, it is a flawed product and I will pass. If it blows up, send it back and move on.

We can't really know what a reviewer's system sounds like or what their personal tastes are. Given that, I think one of the most valuable parts of a review is when a piece of equipment under review is compared to something else. People in general (including reviewers) are bad judgers of absolutes and much better at making relative comparisons, so when reviewers fail to make comparisons to other equipment I find the review to be of little value no matter what's in their system. And when they further fail to list the equipment in their system it makes it even more useless and frustrating. This happens a lot in TAS and drives me up the wall because they review lots of good stuff. Frequently they list their reference system excluding only the corresponding piece of equipment to what they're reviewing. That strikes me as pure cowardice. Anyway...