The biggest disadvantage of acidic fixers are their limited life both as concentrate and working solution. Even sealed commercial rapid fixer concentrate (typically having a pH around 5.5) will sulfur out within a year or two, while neutral or alkaline fixer lives almost indefinitely, even as working solution. A slightly less prominent disadvantage of acidic fixers is, that they etch silver. If you leave a print halfway in acidic fixer, you will detect noticeable bleaching after an hour.
The biggest disadvantage of alkaline rapid fixers is their Ammonia smell. At pH 8.0 and above Ammonia will escape from the liquid as gas, which makes the fixer very unpleasant to use in open trays.
Neutral fixer is mostly odorless, shares the long shelf life of alkaline fixers, and it does not etch silver. Yes, you will need a stop bath between developer and fixer, but apart from that I see no reason to use anything else. Neutral rapid fixer are easy to mix yourself, but also available as packaged products.