I suspect it's a bit like the way overpriced paint protection GAP tyre insurance and all the other rubbish they apparently are compelled to go through with you at the point of ordering.

It's those things that give the sales person large commisions, so are overpriced to suit, all are available for a fraction of the cost elsewhere (for those who have the ability to think for themselves), but they're trying to get you bamboozled and signed up in the heat of the moment.

Was the dealer quoting £350 the same one as sold you the car?

My Roomster (used) was offered with what was presumably the gunk'n'pump set up it left factory with. Told dealer I'd take it as (recently significantly reduced) screen price if they included a spare wheel and jack.

Deal done.

Spare was clean and unused but may have been swapped from another car. OTOH it was supplied at cost rather than faffing about quoting retail prices.

Not everyone knows what to look for, having the dealer offer the right product takes the worry of a mistaken purchase off their mind ... or if a company car then price ceases to be as relevant, if at all ....

Now decide where to put the punctured wheel whilst the spare is in use ... if the spare is spacesaver the full size wheel may not fit the same storage bay and if boot is full of luggage then there may be the need to place it in the passenger cabin. (Still better than being stranded roadside, perhaps in an unpleasant location, or being forced to buy whatever the recovery agent can find, and at an inflated price too)