When you have a web page on the internet that your visitors are going to print, you have next to no information about what printer(s) they have available. Most printers around the world are configured to print out on A4 paper but you can't guarantee that the printer is set up to that default. One North American country uses a non-standard paper size that is shorter and wider than A4. Most printers are set up to print out in portrait mode (where the narrower direction is the width but some may be set to landscape where the longer dimension is the width. Of course each and every printer also has different default margins at the top, bottom, and sides of the page even before the owners go in and change all of the settings to get the printer the way that they want.
Given all of these factors you have no way to tell whether the default printer with its default configuration will print out your web page on A3 with negligible margins or on A5 with huge margins (leaving little more than a postage stamp sized area in the middle of the page). You can probably assume that most will have a print area on the page of approximately 16cm x 25cm (plus of minus 80%).
Since printers vary so much between your potential visitors (did someone mention laser printers, inkjet printers, colour or black and white only, photo quality, draft mode, and lots more) you have no way to tell what they will need to do to print out your page in a reasonable format. perhaps they have a separate printer or a second driver for the same printer providing totally different settings specifically for web pages.
Next comes the matter of what they may want to print. Do they want the whole page or have they selected just a part of the page that they want to print. If your site uses frames do they want to print all of the frames the way they appear on the page, do they want to print each frame separately, or do they just want to print a specific frame?
The need to answer all of these questions makes it just about essential that the print dialog appear whenever they want to print something so that they can make sure that the settings are all correct before they hit the print button. Most browsers also provide the ability to add a "fast print" button to one of the browser toolbars to allow the page to be printed to the default printer using default browser settings as to what is to be printed and how.