I've thought exactly this thing myself. I lurked on an American message board for a while last year and there were women on there who had done half a dozen (or more) tests before their period was even due - then got terribly terribly upset about their lost children. My consultant said that testing too early gives a positive result from ovulation, rather than pregnancy (not sure how that works) - which if correct, means that potentially one isn't even mourning a miscarriage.
The only advantage I can see to testing early is regarding implantation failure. I take suedonim's point that one could wait and be investigated when one has failed to conceive after a certain period of time. However, this may involve waiting (I think the NHS criterion is one year, isn't it?) and the ballpark is wide open as to the cause of one's failure to get pregnant. If one knows that one is conceiving, that's at least one hurdle crossed.
The biggest single cause of recurrent miscarriage is antiphospholipid antibody syndrome, which 'classically' causes miscarriage in the second trimester. However, one manifestation of it (which was my problem) affects the fertilised egg's ability to implant. This isn't detailed in many places, but is described in the British Journal of Haematology.
I was in no doubt from the first moment that I was pregnant, as I felt so utterly lousy (light-headed, sick, stomach upset) - and because of this, tested and have got a positive result as early as 9 days post ovulation. It was reassuring to me to know that this bit was working.
It also meant that, having had three miscarriages, one of which was very early, I was referred to a consultant and medicated. And this in a much shorter time than it would have taken to be referred for failure to conceive.