Limiting inrush current is mostly to protect the diodes as the first
charge the caps. For the first few ac cycles those caps look like a
dead short or mightly close. Under those conditions the diodes have
to stand the short circuit current the transformer can provide which
can easily exceed diode rating if care is not taken.
Also if a toroid mains transformer is used, the transformer start-up
current can be huge for a large (say 1 kVA) transformer, which could
harm the house wiring or burn the fuses in the main distribution
panel.


As far as harming house fuses or wiring, here in the USA and I'd bet
most elsewhere the electrical codes provide for time delay fuses
for surge loads and house wiring that is sufficently robust to
withstand the rated current of the distribution fuses. That should
not be an issue and the power supply should have it's own fusing.
It could be a nusance if the power supply has a massive enough
surge to open the mains fuse but there is not safety issue unless
the mains fuse or wiring is improper.
================================
When switching on an Astron 13.8 V - 50 Amperes PSU ,the surge current
is that high that it (usually)trips the mains 'over-current breaker ' in
the switchboard. I shall now include a soft start facility ( resistor in
230V supply) which is by-passed as soon as DC output is established.

Talking about 'mains fuses' : In Britain and many other European
countries most (modern) domestic supply boards no longer have
traditional (melting) wire fuses but (resettable) fast acting 'over
current' cut-out devices .
There are 100 Amperes wire fuses in each phase of the incoming supply
cable ,but these can only be replaced by the electricity supply company
,since these fuses are each fitted inside a separate 'wired-lead-sealed'
box.

BTW the over-current breakers are separate from earth leak detection
cut-out devices ,officially called residual current detectors (RCDs).

Frank GM0CSZ / KN6WH