[link to pointless blog post removed] This might help you know why you have to wait for a PR update .
I think you are confused. PR is not site wide. Every page gets its own PR calculated. And, according to Cutts, PR is calculate daily and always shifting. The public PR we see, is just when they decide to push their current calculations to the public. I doubt it takes hours to calculate for a single site. Once they have crawled the site and indexed the page, the information is all right there, where it links, meta's, who links to it, content, etc... etc... They can easily calculate pagerank as pages are processed into the index, and then update it later as new links are found, considering how many servers and data centers they have. I don't think it takes 3 months for them to calculate pagerank. People are not waiting for google to process data that takes months to process. Google is always processing this data. People are waiting for them to make this information public. I can dig up Cutt's quote if you want, but nothing on that site is backed up, and you can look up Cutt's quote too.