It does seem unusual. 
Ds' school pretty much offers an AH in every subject - it will vary from year to year, depending on what the pupils themselves want to do. Off the top of my head, I can think of ds and his friends who are currently doing AHs in English, History, Maths, Physics, Chemistry, Biology, Graphic Communication ("core" if you are wanting to study Architecture or go to Art School), Modern Studies, French, Spanish.... (and that's just with ds mentioning subjects his friends are doing in passing for example, he's glad he doesn't have to do the reading involved in AH History
) If it doesn't have sufficient numbers or there is a time tabling/resource issue, the pupils will go to the local college for that subject. On occasion I think they have even had pupils from the local private school joining them (and vice versa).
Glasgow City Council also organises an AH Hub at Glasgow Caledonian Uni so that pupils at schools that don't offer enough/the required AHs can go there. (I don't think ds' school is eligible for that scheme as it is expected to be able to offer the AHs itself ).
A friend's ds at an East Ren school is doing an AH in Music (not sure what else he is doing - just know that he's going to Uni to do Music)
The SQA offers c30 AHs (excluding the ones in Gaelic), which would pretty much cover any subject you wanted to do at Uni. Some of the AHs are for subjects you don't need to have done to AH as you can start them at Uni (eg Economics, Statistics, Accountancy)
Not all "good" English Unis require 3 AHs. Oxbridge might - but they are always a special case and they will often customise requirements. I looked up Leeds (as they made me a conditional offer many many
moons ago, when I applied direct from S5 didn't go there in the end as I went to my first choice of St Andrews ) and this is what they said for SQA exams (in the attached picture)
On the other hand, even Scottish Unis require 3 good AHs if you want to study subjects like medicine or Veterninary Science. So on that basis, your dd is indeed being disadvantaged
- not by the SQA system but by your local school/local authority 
Don't be too negative about the opportunities to study abroad - from what I recall about, for example, French education, most continental exam systems don't expect the degree of specialism involved in English A Levels. The French bac is much broader, even though you end up choosing an Arts based or Science based one (which is over simplifying it
)
It's also worth looking at wigglebeezer's suggestion of the Open University's Young Applicants courses.
FWIW - I agree with you about the stupidity of stopping Geography at the end of S3 (which is presumably when your dd's school starts its Nat 5 time tabling). It must also be very boring for their Geography teacher(s)
Ds got an A for his Geography Higher and in S4 was considering doing a Geography/Geology degree (in S5 he was wanting to do Maths/Physics and in S6 decided on - and had been accepted to do - International Relations
the joys of teenagers changing their minds
)