A lot of variables really.
Some people use a travel agency that can negotiate on your behalf.
I know people that keep a bag packed and try to do what you said, but not 2-3 weeks prior, more like 2-3 days prior. Idea being the cruise line would rather have a cabin booked for some profit rather than empty all together....that can entail being flexible on trip itinerary as well.
We live in Florida so it’s possible to do that because several ports are within driving distance.
We liked the Caribbean so we avoided hurricane season.....our rule of thumb is no cruise later than June.....preferably April or May. Those months are considered peak but it’s better than experiencing rough weather.
Best cabin we ever had was arranged by a travel agency provided by my employer free of charge. The travel agent booked the cruise but didn’t reserve a cabin as he was angling for an upgrade.....a week before the cruise he called and sure enough we were upgraded to a balcony suite complete with king bed, jet tub, a sitting area large enough for a couch and chair and a wet bar. The balcony was large enough to accommodate two full size lounge chairs ....that was without a doubt the best cabin we ever had. 😏
“I know people that keep a bag packed and try to do what you said, but not 2-3 weeks prior, more like 2-3 days prior. “
When we lived an hour north of San Pedro, we were on a list to get those last-minute offers. Same thing ... had bags packed under the bed, and all ready to go.