Owning your own home

We kind of did. We needed to move, and schools played a big part in the location 1/2 mile away.

Suppose a huge chunk of SDLT is cheaper than private school fees in the long run.

The problem with "catchment areas" is that unless the school is so large (or the catchment area so small) that it can guarantee that everyone in a certain area gets in then it'll end up coming down to distance-to-school as a tie-breaker as there is usually a huge variation in intake between years.

Some of the local primary schools around us have been as low as 120m once siblings have been given their precedence.

Also, if this is the case, then this will often be priced in to the properties close to the school.

(MiniGB's old primary moved to a ballot rather than distance-to-school to help get away from this system gaming.)

Yep: We moved about a mile to make sure eldest got into an OK school.
Our old place - which we loved - was about 50m outside the "catchment area" of the only school we really liked.
There was no guarantee which school the eldest would have got into - there is no such thing as school "choice" in those situations.
We looked at renting our place out and renting somewhere nearer (but they've rightly put a stop to that), and also buying a second smaller place with the view to returning to the original place a few years later.
In the end we sold up and moved. At great expense and stress.
Eldest will start at the school we wanted in September. But she actually won a music scholarship to another OK school, and I suspect if we'd stayed in the old place she would have got in under furthest distance as demand each year is different.
But hey!