Hi MikeTB,
You raise quite a few interesting points.
The good thing is that we can let the roadside breakdown service look after problems, at least for 3 years anyway.
The sealant/compressor systems do work, but not something you would like to do at the roadside, unless you were really stranded.
Having said that the compressor is handy for many things, and enabled you to keep mobile on the day. The aerosol TyreWeld is unlikely to have re inflated the tyre. Any sealant system must only be regarded as a temporary repair. OK a small screw is fortunate but something a bit longer could cause unseen damage to the casing of the tyre and cause a failure later. Moisture can get in to the structure through the hole and again result in a subsequent failure. The tyre should always be removed from the wheel as soon as possible, inspected and have a permanent repair, typically a 'mushroom' plug applied through the tyre from the inside to seal the hole. This is covered by a British Standard which defines where it is possible to do this on the tyre. It is possible to remove the approved sealant from within the tyre to effect a satisfactory repair. However, it is not something that all the tyre trade is willing to do.
Car manufacturers have approved tyre sealant systems instead of spare tyres/jacks etc in the constant quest for weight/fuel saving, but only after extensive testing of products over the last 20 years. They are now the norm for Mazda/Honda/Nissan/Toyota/BMW/Mercedes/Audi/VW.
They do have a place, particularly with ever larger wheels/tyres which are not the easiest of things to change, assuming you have been able to jack up the car safely and remove the studs and get the wheel off at all.
Having said all that I better go and get on with my retirement.