Storing a telehone number in some kind of canonical format has several advantages from a programmers point of view, but it might confuse the user, if sudde
The main difficulty in canonicalizing phone numbers is determining the correct canonical format. Different countries have different ways of grouping numbers - and within a country, different numbers can be grouped differently.
It used (once upon a decade or more ago) to be that case that in the UK, you had 01-234-2345, 021-234-1234, 0334-234234, even 092324-213; things are different in the UK now - generally more digits, and I'm not sure about the groupings any more (absence makes one's knowledge less current).
Dealing with country prefixes and indicating the internal country dialling prefix is fun: +44 (0)1394-726629 is a UK number, country code 44; dialling from outside the UK, drop the 0; dialling inside the UK, do not include the international prefix but do include the 0. Do note that the form with (0) in it is in fact not valid if you follow the E.123 standard.
This is similar to the problem of canonicalizing mail addresses - not as complex, but still bad.
Also, as noted in my comment to HeavyWave's answer, forcing people to enter the phone number as a digit string with no punctuation is nasty. It's fine to store it that way; just present the data in a human readable format. There's far too much lazy web form programming out there.