Why don't inductive spikes get through a transformer?

Well, a spark, not necessarily a massive voltage spike.

There is a voltage spike on the secondary of the transformer. In a classic transformer-rectifier wart, it is reduced by

Leakage inductance

The 10x or 20x turns ratio

Any secondary load

the rectifier/filter on the secondary, if present.

Load current has very little to do with the energy storage because the current in the primary and the current in the secondary are opposing. It is the primary magnetizing current and any attendant leakage current that are the storage mechanisms.

You'd only get a spike on the primary to the extent that the flux is not linked to the secondary where current can flow. But, since it's not linked to the secondary, there's nothing to create a spike there.

Sylvia.

I assumed if there was 1000 volts generated on one side, the transformer would convert that into the relevant voltage on the other side. But I've been told elsewhere this spike would happen so fast it would be the equivalent of very high frequency, which transformers don't pass too well.

Same effect. A primary spark is usually created by energy stored in leakage inductance, and leakage inductance reduces high frequency coupling into the secondary.

You can Spice that.

Have you even looked at a model of a transformer? You can find them online. If you know as much as your question seems to intimate, then you could probably see the answer yourself.

My car seems to think you can pass it.

Made of lego?

How could you possibly know the level of my knowledge?

Made of mathematical equations. You can find a pretty good one in LTSpice.

John Larkin isn't very bright, and doesn't seem to realise quite how enthusiastically you advertise your incorrigible pig-ignorance.