if you were signing up with a host, would you prefer that the host offered 24/7 support and then was never around or a host that offered dedicated support times and then when available replies or major issues out of hours?
Would you rather be dissapointed or no the truth from the start even though you are aware you wont be able to get constant support?
Well, if someone (Bob) were to order a shared hosting account from a host then I would hope that he would test the company's support before ordering. However, if Bob did not do that (which I assume is the choice of the majority of web hosting consumers), I believe that Bob would order based on the hope that he would receive 24/7 support.
Eventually when Bob goes to look for the support at 3:00 a.m. he will be dissapointed. However, even if he chooses to leave his current host, he will go to another host that claims to offer 24/7 support. Due to his 3:00 a.m. problem, he is going to want a host that will actually offer support at that time, not a host that offers support from 9 a.m. to 5 p.m. Nonetheless, this time he would hopefully test this new company's claims.
Thus, that is why many hosts that are starting out claim 24/7 support when it is not true. They snag Bob as a customer and hope that he goes to sleep at 9 p.m. and doesn't wake up until 4 p.m. (after school is out).
24/7 support doesn't necessarily mean 24/7 live chat or phone support, however. Many hosts say that they offer support via live chat and phone during normal business hours and ticket support after that (which isn't a bad thing). Yet, some hosts do that and "guarantee" a 6 hour response time on tickets, so would you consider that 24/7 support?
To me, when someone says 24/7 support, they should specify the methods (24/7 by ticket system, email, etc.) and make sure they can back it up. Else, the company should really rethink the 24/7 support idea and get real with the customers on what their true support hours are for their base.