You can give thrombolytics up to 12 hours after a Myocardial Infarction for the bottom line reason is that there is still a measurable Mortality Benefit.
Also, Factor XIII or clot stabilizing factor takes longer than 12 hours to ‘stabilize’ the clot a render it invulnerable to lysis by plasmin. So, the first part of your question about taking 3-6 hours for the coagulation system to break down a clot is not accurate.
The brain has no GLycogen stores, hence,irreversible damage occurs after only 3-6 hours. There is no point in re-perfusing dead tissue. Like sending flowers to ex-husband five years after divorce.