You're right that it sounds like parallel should be better in theory, but here's what happens in practice...
The A/D-D/A conversion in the effects unit causes latency - a short time delay, so the effected signal is out of sync with the original - and which also applies to the dry part of the signal via the processor in almost all digital processors (some do keep the dry path analog, but most don't). This is usually so short that it's not noticeable as an audible delay, but... if you then mix it with an undelayed dry signal, you get a nasty 'comb-filtering' effect like a stuck flanger. Depending on the exact latency and so where the notches in the comb filter fall in relation to your note frequencies, at best it makes the tone just a little worse, at worst it screws up the tone and volume completely. You can get around it by having the FX unit set to 100% wet, so there is no delayed dry signal to mix with the undelayed one, but this is only possible if you only have one FX unit in the loop (since each one needs dry signal to work with, not just the effect portion of the previous unit), and then only if you want to be stuck with one wet/dry mix, which is not likely to work if you use different programs.
What's worse is that the Mesa parallel loop is quite crude - in a well-designed one, you can cure all the above problems by turning the loop mix up to full (no dry signal), which effectively makes it series. But the Mesa loop works simply by feeding both signals to each end of a single pot track, so neither can actually be turned right off, just reduced to a low level. This low level is still enough for the latency effect to occur. Even worse, it can also allow some signal from the FX unit's output to feed back to its input, which exaggerates the problem even if it doesn't cause stability issues.
Even with analog effects, there can sometimes be problems with phase (some FX units have their outputs out of phase with the input, which is again not noticeable in normal in-line use) and feedback.
*All* these problems are eliminated by simply removing the dry path through the parallel loop, and so it's a common mod that many people do to their Mesas... Mesa have just finally taken notice.