Good question. I know what you are talking about - but I'm not sure. I'm going to google this because I want to find out as well.
Are you working with a WP blog or a CMS or a plain webpage with scripts? It all makes a difference. -Howlinghawk
Google has definite crawl budget. Priority is on scale of 0.1 to 1.0 ( 1.o being highest ) It indicates the importance of a particular URL relative to other URLs on your site. Change frequency is a hint how frequently content is changing ( hourly, bi hourly, 8 hourly, weekly, monthly , etc ) Having said that, the crawl frequency, depth of crawl is algorithmically calculated by the engines from information collected by the crawlers and it can ignore your sitemap settings.
Sitemaps provide additional information about your site to Google, complementing our normal methods of crawling the web.
for google Priority Change Frequency Last Change doesn't matter and google don't follow instructions at all ... what google want frm you is just a sitemap
You can find more detail about sitemaps and the elements here: sitemaps.org/protocol.php They are pretty general details, so they don't really tell you how Google works, but they do describe what the elements mean and how they're supposed to work.
I do understand what they mean and if google paid attention to them i could see why you would want them there....but i wonder if it actually makes any difference in real terms. The main reason i ask is i use a free sitemap generator that works well with crawling and generating the sitemap, except it doesn't have those attributes. All the free sitemap generators (and i mean for over 500 pages) that have these features don't actually work very well. They always crash half way through crawling. My gut instinct is google will decide itself the value of each page due to the site structure and links. It will also decide itself on change frequencies. This would make these attributes unnecessary. Unfortunately this is not based on anything except my opinion so could be way off mark.