If TB were a problem in the UK goat population - DEFRA would have us testing compulsorily until the cows (goats) come home!
The reason I would tread very carefully with this is
a) freshly kidded goats really don't need any stress and unless the vet is any good at injecting/taking blood/causing pain in any way it can cause massive stress to them - if you ever had to inject a goat as opposed to a sheep...
b) Goats do not normally stay outside during the night, are indoors on wet days and for most of the winter, and their sheds are normally properly enclosed (unlike most cattle courts). So I don't think there is much of a risk of cross-infection.
c) Actually the fact that there only ever was ONE proper outbreak of bovine TB in goats is a case in point - there are large numbers of goatkeepers and a few goat dairy farms in the South-West if the risk was here DEFRA would test. No outbreaks - so no problem. It could create a bit of a hype amongst the general public if we started to test our goats all of a sudden. (And please don't give DEFRA ideas... I already pay well over 200quid each year for my CAE tests - and I KNOW they are negative before they get done!)
d) There is a significant proportion of cattle that react positive to the test, get slaughtered only to be found not to be infected after all.... except than it is a bit late isn't it?
Actually I think one of the main reasons that TB has not been researched and overcome in cattle is the fact that the milk is safe once it's pasteurised. If that were not the case the government would have had to spend much more and solve the issue... this way, it's only cows that get killed and it's cheaper to re-imburse the farmer the meat value... sorry a bit cynical there