It's a ghastly aeroplane, which is why most instructors like it
It's stall behaviour makes it good value for money compared to a hairy fairground ride.
You will not want to (or be able to, probably) rent it when you have your PPL, so why train on it? Train on something similar to what you will be renting later. That simple decision will save you £ four figures later on and you will end up being a reasonably proficient pilot on your first solo outings, having had 50-60hrs on the type, rather than trying to get used to a new type, as well as everything else you have to do.
Currency on type is 90% of the job in flying.
All PA38s I have flown in (I have 20 or so hrs on them) also happened to be in terrible condition, with leaking seals, full of water, smelling like a public loo, and had a useless elevator trim. Trim is another very important thing in flying, affecting pilot workload substantially. I walked out of that school eventually, having got sick of appalling maintenance practices where bare wires were left hanging out in the engine compartment.