Well they say you should check your tyres weekly for tell tale signs of sealant leakage so you know that the tyre has been penetrated. If you see a nail head you would want to remove it and not leave it to maybe "work" it's way out at some stage. Then the sensible course of action would be to get a proper repair done.
They make the hole bigger to get a better fit to the plug and then the internal flange is vulcanised to make a well sealed patch inside the casing. With the old external kits you used to fit plugs with a metal hooked spike you also had to make the hole bigger. I used them years ago on crossply tyres when they were thought to be a safe repair, but that's all changed now.
I can understand why they wouldn't give you one for a swing. People have paid for disposal, they have to account for them, they're under a legal obligation to dispose of them properly. They couldn't give anybody something to take away without a waste disposal licence and you could be an environment agency plant. Tyre disposal is a funny business and there are dumps all over the country with thousands of tyres with little hope of recycling. Just look at the fires that make the news together with the criminal gangs that flytip lorry loads of tyres. Would anybody do that if there was big money in actual proper legal recycling.
