It may be good idea, but it wouldn't be cost effective.
We do not know, actually, which titer is how much protective, and to whom, and in which situation. Titers are "that second" measures, and they are relative. Furthermore, they do not predict IG M=> G=> A "surge" should the patient gets exposed to virulent agent. Pregnancy, recent flu, that recent pack of Medrol (yeah, you know it was not that needed but you had to work with that sinusitis) - all can affect them, in poorly predictable way. And, if they run low, you are going to get a shot (not a big deal, but still $$) and then more titers =>> see above.
On the other hand, for example, MMR induces "protective" titers for measles in about 95% of healthy recipients. We do not actually know what happens with remaining 5%. Everything we do know is that they are "serologic non-responders". Statistically, only like 10 to 25% get clinically sick if exposed. What happens with the rest is not exactly known except that they do not get clinically sick while not developing protective antibodies of the class(es) we look for if exposed to "wild" virus. We cannot do anything with this facts, and the numbers stay the same for decades.
This is the reason why workers in areas of "very high risk" exposure (like vets and military) are just mandatory vaccinated without too much hassle with titers.