As Atmasphere pointed out, there are certain inherent limitations of transformers. But, that is true of ANY means used to amply the signal of a low output MC cartridge. If an additional active stage is needed, that too, has its problems. Unlike a transformer, any active stage will increase noise. It is easier to control noise with solid state devices, but, solid state has a particular sonic signature that some may prefer to avoid.
My own preference is for tube-based phono stages. However, that usually means an extra stage of amplification over an MM phonostage or the use of a transformer. Part of the problem with transformers is that they need to be carefully matched to the particular cartridge to work their best.
The other "problem" is that really good transformers are NOT CHEAP. I've heard great sound from Audionote (uk) and Kondo stages that had breathtakingly expensive transformers in them. I heard homemade units with the Audionote transformers that were also terrific. Another transformer that sounded good to me is the Jensen. My own phono stage (Viva Fono) has a transformer in it, but I don't recall its provenance.