If you look carefully at the cap-free LDOs you will find that
their overshoot specs (if any) are tied to an input voltage
step or an output load current step whose characteristic
frequency (like 1/t_rise) is lower than the loop bandwidth.
Which is fine as long as it's realistic, but many applications
can impose faster load steps than these regulators on their
own (i.e. with "zero" capacitance) can truly handle. It's a
marketing play in large part, getting people to spend money
on your IC instead of somebody else's capacitors.
Capacitor quality matters as much, maybe more, than size.
Specifically ESR & ESL. You may not need the caps that
remain, to hold up for long (depends on loop BW) but you
would like them to hold up well for that period, and ESR
makes for a pedestal jump while ESL makes the cap slow
to do its part initially.
Challenge any idea that you should, or even would benefit
significantly from, eliminating 1 or N capacitors. Presumably
your load devices will still have close-in decoupling per
best practices, so there's a minimum pool of filtering cap
regardless. Then, what's (say) two more, big and little
high-Q ceramics? Also there is a minimum ESR/ESL for
some LDOs to obtain stable operation, need a HF zero to
keep the poles in check.
Again, since the overshoots will always be present, you
need to quantify what's acceptable, and add design margin,
and work to that.