The disadvantages would be the potential frequency in which the tailor visits for the subsequent fittings. They won't just measure you up and then finish the suit AFAIK, unless you are a repeat customer.
Travelling bespoke tailors like the ones listed above are not MTM, unless they offer a MTM service.
MTM uses a block with standard sizes such as 46S/R/L and from that block they adjust shoulders, sleeve length, inseam, rise etc.
Bespoke will cut a pattern from scratch...