yep, not cheap.
I have been told there arre massive fines for tampering with it in the USA.
Down here we just cut the buggers off.
A fuel tap gets put onto every mower that comes through the shop for a couple of reasons.
Firstly it allows the filter to be replaced without having a fuel bath and secondly it allows the owners to turn the fuel off and let the carb run dry when they will not be using the mower for a while.
Before you do any thing drastic, you can replace the fuel solenoid ( which might not be your problem ) with a standard bowl nut which is only a couple of $.
Check that the choke is coming on fully.
If the cable is not anchored in the right place the cable does not have enough pull to apply the choke so the engine will not start from cold.
Then there is clean fresh fuel. Modern fuel (which is not petrol ) goes off very quickly and it looses the bits they put in to allow carby fitted engines to start.