Persistent connections are far more complicated to reason about. I believe what you mean is that this makes it more difficult to scale PHP, which is arguably true, but at the same time it forces you to understand underlying concepts.
e.g. A 'ALTER SESSION'/'NLS_DATE_FORMAT' commands in Oracle or even an unfortunate 'USE <db>' w/MySQL.
There are of course safe solutions & techniques for this, but when you have an otherwise stateless-by-design codebase (such as with PHP), picking up "possibility state-laden" connections is a bit of an unexpected concept that I've seen catch developers more than once.