I shall help build bridges here

If you are concerned with breathing then use a home vac with a filter and open a window once in a while.
Addresses and answered (and
PROPERLY answered, btw) here (emphasis, mine):
For general "don't want to get my garage too dirty" dust collection, Howards's shop vac method is fine. IT WILL NOT PROTECT YOUR LUNGS FROM EXPOSURE TO FINE DUST PARTICLES.
Trust me, I have severe Asthma, if the dust was THAT bad when using a typical vac then I wouldn't be alive.
Several important points were glossed over in response to what nos has stated. Again, emphasis, mine:
If you are concerned about the health risks of breathing WW dust, check out this site.
http://billpentz.com/woodworking/cyclone/Index.cfm
If you are serious about woodworking, real dust collection is a must. At a minimum, a good quality respirator, with particulate filters is needed.
It's not an instantaneous problem, that's why they're health "risks", not "fatal consequences". Since you're telling us you have serious asthma, I have no doubt you will readily admit that even with your minimal dust collection efforts, your asthma is still affected.
I'd like to state that your suggestion
IS better than doing nothing, but as nos is pointing out, if you're SERIOUS about woodworking, that suggestion is a "gateway" to
real dust collection, and not as effective as
real dust collection in conjunction with breathing protection of some sort.
I hate to disagree

STOP IT! You're KILLING us here with your jokes! BRILLIANT!

but that thing is just a glorified Dyson vac with a hepa filter.
In reading that statement, one could take away the idea that you believe your shop vac method is just as effective as the "glorified Dyson". The CFM and particulate removal of dust collection systems are SO much greater that it isn't a fair comparison of the two methods. There is a reason that such systems are in use, rather than a cadre of shop vacs hooked up to the blast gates at each tool station in a "professional" shop, and it isn't just convenience.
It's also a chicken/egg thing. These systems were around long before a Dyson was created. My guess is that's why Dyson adapted it for a floor vacuum. In effect, you've stated that it IS the best system, you just haven't realized it yet.
All that being said, there won't be many people here who will EVER take their woodworking to the level where they should look at a cyclonic dust control system, but to pooh pooh qualified, accurate, factual information with a "that's just a glorified Dyson and woodworking dust isn't THAT bad" is as detrimental as the opposite extreme of someone saying "you simply MUST use this system or you're going to die!".
Nos gave a single link. If you wish more, I'm sure REAMS of information can be found and provided to back up his assertion of the hazards of particulate matter in woodworking, the effects of it, and the increasing degrees of removal of such matter by various means. Your shop vac suggestion will be on the lower end of the scale in effectiveness. Better than nothing, and several lesser methods, but far from being as effective as a "glorified Dyson with a hepa filter".
There's a rather large base of information to back nos up. This isn't just a matter of opinion and your asthma being the deciding factor.