If I understand correctly a fertilized egg will not begin to develop until it begins to be incubated. Therfore keeping them on the counter will not reveal any developement after, say, a week when you go to make an omelet... if suddenly you had a broody on your hands how long could fertilized eggs be setting on the counter and then set under a potential mama hen... Which brings up my next question. Can I tell if an egg is fertile before begining incubation without cracking it open?...
Eggs that have been sitting on your kitchen cabinets are poor candidates for producing chicks. Your wrong about when chick development begins.
Chick development begins at much lower temperatures than those temperatures encountered during incubation. This SLOW development saps the egg of its vitality. Only eggs that are kept under the best conditions to preserve fertility and viability should be set.
Eggs stored under the absolute best conditions for 14 days will only hatch about 50% of the time. Most hatcheries will not set eggs older than 7 days old because eggs older than 7 days start falling off the hatchability scale real fast. You can forget about hatching 3 week old eggs because after 21 days those eggs are not worth the wear & tear on the old hens' you know what.
Do this, store your eggs under the best possible conditions. Since ALL eggs destined for hatching should be marked with the date that they were laid, put these eggs aside and store them as possible hatching eggs. Every day remove any egg from storage that is older than 15 days and then you can let those eggs sit on your kitchen counter till the cows come home if that makes you happy.
The best conditions to store eggs are @ 65% humidity
about 55 degrees Fahrenheit
In a dark location
away from spikes in temperature
and vibrations like on top of or near a dishwasher, clothes dryer, washing machine, refrigerator, or microwave oven, and whatever you do TURN your eggs once, or three times every day but never turn your hatching eggs twice in one day.