I've not found that transformers contribute to transparency. IME they always detract from it. Bandwidth aside that has been the main reason I avoid them if possible.
Distortion is however a main reason people will often prefer transformers, as these days of inter-stage transformer use it is mostly in single-ended circuits. The type of distortion I am referring to is the lower ordered harmonics, the 2nd, 3rd and 4th.
We have built a number of OTL guitar amps, and one of the problems we ran into was the fact that the amp was transparent and not a lot of distortion. This is great for a high end audio amp but bad for guitar. So we built an OTL that used a single-ended driver circuit and an inter-stage transformer to go from single-ended to push-pull. This got us a lot more 2nd ordered harmonics, which made the amp sound richer.
Sunn used this technique in their early transistor guitar amps, which have a reputation amongst guitar players as one of the few transistor amps you can use with electric guitar, due to the richer sound of their single-ended circuits (which were also mostly zero feedback).
When you are using a transformer for audio purposes, loading of the transformer is a big deal. If not loaded at all, the transformer will merely express the inter-winding capacitances rather than the turns ratio. This will result in poor bandwidth and distortion. As you load the transformer more and more, approaching a value known as 'critical damping' that bandwidth will widen and the distortion will drop. Because there is not a lot of power involved, the bandwidth of the transformer can be quite decent, easily exceeding 100KHz, so the real issue is how well it plays bass.
In SET circuits this is usually not much of a problem because once you get above about 7 watts or so you aren't going to see much low frequency bandwidth out of the amplifier anyway. Plus, to take advantage of the SET's ability to have unmeasurable distortion (in a lot of SETs distortion decreases linearly to unmeasurable as power is decreased towards zero) you need a really efficient speaker (103 db or more) and you are not going to get much bass out of most of those speakers either.
In order to get a condition of no phase shift in the audio passband (20-20KHz), the amplifier must have bandwidth from 2Hz to 200KHz, IOW 1/10th to 10X of the frequencies to be amplified. There are very few tube amps with bandwidth to 2Hz, and not many speakers that go to 20Hz, so this bass thing is where most of the fudging occurs in tube amplifier design, which is exacerbated when interstage transformers are employed.
Phase shift in the bass region translates to a loss of impact to a frequency up to 10X the frequency of the cutoff. So if the amp rolls off at 15Hz its a problem up to about 150Hz or so. This is the other main objection I have, as the speakers I play at home go to 20Hz. I played bass in the orchestra for a long time and as a consequence I have found that I am hard to please in this regard, hence I stay away from transformers in general.
