given how rare fire is these days in F1 i'm surprised this hasn't happened earlier, off shore power boats went with the F16 canopy quite a few years ago and it's made a huge difference to their safety record. the FIA seem bent on making F1 a non fatality sport no matter how impossible that maybe and given how drivers drivers are these days walking away from impacts that should at the very least result in major fractures, the head is the only area left for them to worry about.
i'm not a lover of loosing open cockpits but these days there's so much driver protection each side of their heads that maybe it would actually allow the spectator to see more of the driver.
biggest downsides i'd have thought will be that aero efficiency will improve so we're probably looking for a further power reduction to reduce speed (though they might use some lateral thinking and control top speed with a aero drag fittment which could improve slip streaming) and how will they cope with dirty windscreens or wet weather? F1 pitstops are too short for pit crews to clean like in prototype or GT racing, a wiper probably won't work on such a tight curvature and even a rip off may be awkward given the shape. then there will be the problem of heat build up, sitting in a small green house in the middle east in fire proofs is not a good way to stay cool, F1 cockpits are already very hot, fighter cockpits are uncomfortably hot in sunshine, put the two together and it could easily be unbearable. and of course at some point, no matter how unlikely, someone will end up upside down with the car jammed in a barriers/ tyres with enough room for a driver to crawl out but not enough for the canopy to be removed and there will be a fire.
on balance i'd say F1 is pretty safe these days, driver's helmets and crash protection does an incredible job already, so we probably don't need this given the potential problems and how it would fundementally alter the look of the cars.