A friend's air conditioning has failed and she doesn't have the money to
replace the compressor etc.

So she's looking at so-called portable AC One unit she saw looks nice,
has the right controls plus remote, but only has an output hose. One of
the laymen reviewing it makes that a deal breaker, that it doesnt have
an input hose also to the window.

Because this means it will suck hot air in from the outside, but that
won't be the same air expelled.

This makes sense to be but maybe it's not as bad as the reviewer makes
it sound. If hot air is sucked in through its own hose, the AC won't be
able to add as much heat to the hot air as it would to te room
temperature air, and that will lower the efficiency of the AC. It will
also lower its speed of heating the room it's in, although it will raise
to some extent the temperature of the rooms it's not in, depending on
where the outside air infittrates.

Normally she keeps the basement window (10 inhces high near the ceiling
of the basement) open all summer, and the other major place is the mail
slot in the front door. It has an inner metal flap and an outer metal
flap but no foam in either flapway. (Maybe if I looked at it some more,
I could figure out how to add foam that wouldn't either keep the mail
out or get knocked off by the income mail.) Also the weather stripping
in her laterallly open window probably won't work as well when she has
to open one window and one storm window for the hose output.

Do you think one hose AC is terrrible and should avoided at all cost?

About half of the machines out there are one hose. Admittedly, the
cheaper ones, but she doesn't want to spend too much either.

Her b-room is 14 x 19 = 266 plus if she leaves the little bathroom door
open that's about another 30 feet2. IOW about 300 sq.feet.