Till now probably there is no evidence of whether we should use aspirin alone in Covid 19 patients to prevent blood clot unless he is suffering from some cardiovascular
disorder . This may be probably due to no well conducted RCT taking aspirin into consideration. Although there are suggestion it can be useful. Earlier there were claims that use of NSAIDS were associated with adverse respiratory effects but as concluded by WHO currently there are no such evidence.
There are many antiplatelet drugs which are superior to aspirin thus making them a relatively better choice. Regarding antithrombotic therapy, in presentations consistent with ACS due to plaque rupture (i.e., type 1 MI), dual antiplatelet therapy and full-dose anticoagulation as per the American College of Cardiology (ACC)/American Heart Association (AHA) and ESC guidelines should be administered, unless there are contraindications. If there is high prevalence of bleeding less potent antiplatelet like clopidogrel should be used. This point signifies that antiplatelet drugs has been used for prophylaxis together with LMWH and since there are better drug than aspirin they are preferred. (Remember, by prophylaxis, I mean that when patient is admitted to hospital, at the same time treatment is given because inflammatory conditions and coagulation cascade take time to occur. But if one is late for admission antiplatelet drug can be benificial if already taken.)
Currently, the standard therapy for thromboprophylaxis in thromboembolism associated with COVID-19 is LMWH.
This paragraph is a little extra, may not be specific to the question, non interested users may skip. The microvascular clots and microvascular pulmonary thrombosis is associated with the inflammatory condition. One of the main protagonist of this inflammatory condition is IL-6, there were trials of tocilizumab, a monoclonal antibody against IL-6, but the trial did not meet its primary endpoint of improved clinical status in patients with COVID-19–associated pneumonia or the secondary endpoint of reduced patient mortality. The trial did show a positive trend in time to hospital discharge among patients who received it(Tocilizumab was in use in areas I know before the result came). It was hypothesised to be useful in preventing hypercoagulation.
Now, coming up to your point :-Can aspirin be used as a prophylactic measure?
Well, antiplatelet drugs can be used for prophylaxis of thrombotic condition especially of arterial etiology ( like atherosclerotic plaque) as I mentioned above but there are many superior drugs for use than aspirin amongst the antiplatelet drugs to use. In this article it is mentioned that COVID-19 patients taking low dose aspirin for secondary prevention of cardiovascular disease should continue their treatment.
Aspirin has some other limitations too, which might have been taken into consideration for initiation in non cardiac patients instead of anticoagulants like LMWH:-
The drug irreversibly inhibits platelet cyclooxygenase, and its effect persists for the circulating life of platelets making its use controversial in COVID-19 patients.
Aspirin is not indicated for the treatment of DIC, or other venous thromboembolic complication that might be associated with severe COVID-19, and may increase the bleeding risk in severely thrombocytopenic patient.
Lastly, if one talk about taking aspirin even before having any symptoms of Covid 19 the person need to be concerned about risk ( risk like increase G.I bleeding related to aspirin inhibiting substances that protect stomach lining , allergic reaction) of daily intake of aspirin . Normal person if hospitalised, is recommended with use of LMWH, which itself becomes a prophylactic measure and will be enough to reduce thromboembolic condition ( Covid patients were at higher risk of venous thromboembolism that prompted us to use LMWH instead of antiplatelet drug) related mortality in a normal person. Although, in person with coronary artery disease and already taking aspirin, together with LMWH in hospitals can help to reduce mortality.