Now If the single runway at the alternate became blocked and there were no other alternatives. I would declare a fuel emergency and if necessary if the taxiway was long enough I would land on it.
I was thinking exactly the same ref' the taxiway. A suitable strip of tarmac in an emergency is a suitable strip of tarmac. However, why not apply the same thinking at destination? If Wx is OK and there is an EAT which dips into diversion fuel, but not the last 30mins, and ATC are aware of your status then why not wait. An emergency at destination, or an emergency at alt'n? The statisticians will tell us if there is a difference. It can be argued that waiting at destination will give you more fuel when the emergency happens than at alt'n, where you will arrive with only 30 mins.
Expanding the debate: you are in descent to destination passing FL150. You are arriving with RES Fuel. Wx is fine & at alt'n. The alt'n is beyond destination and requires an overfly. You are now alerted to a 10-15min delay. Decisions? One thought might be to remain FL150, reduce to min clean and proceed to a point midway between destination & alt'n. This could be a convenient point about 50nm from both airports. Luckily convenient. Decision time would be at that point having eaten up some of the EAT delay. You'd land at alt'n with >30mins or land at destination with <res. Some thought would be given to if you are now No.1 into either airport, i..e the runway is clear & open.