I can't believe this discussion has popped up again after only two weeks! As mentioned, asthma is a response to various factors, could be heat, cold, chemicals, pollen, exercise etc., which is presumably why it precludes you from joining the services (you might not be able to guarantee control in all situations). Just because someone can't join the services because they have asthma it doesn't mean they are unfit, it just means that they are not fit to join the services, just the same as someone who doesn't meet the vision requirements for firearms. Exercise-induced asthma exists, although it can be difficult to separate this from pollution-induced asthma if you are exercising in the pool or outdoors.
You are unlikely to be able to do strenuous exercise unless you have good control over your asthma and it could in fact be extremely dangerous, as your lungs may not be able to get enough oxygen in. I'm not a doctor, but my understanding is that this can ultimately lead to cardiac arrest, but sometimes it can just causes someone to hyperventilate. I suppose it's possible that if you ALREADY have good control that exercise could improve your control. I myself have found this to be the case, but there are times (there is a lot of pollen or pollution, I have a bad cold) when I do need to take reliever medication either before or during heavy exercise.
General consensus among scientists seems to be that the common asthma drugs used in asthmatics do not increase performance beyond what is to be expected if used in line with the recommended therapeutic regime, and would also not improve performance in non-asthmastic individuals if used at those levels.
To say that asthmatics are simply unfit is dangerous in my opinion, because it could discourage children playing sport at school from taking their asthma medication.
Have a look at www.wada-ama.org/rtecontent/document/Asthma_en.pdf if you want to read a more scientific description.