Also, even if they sincerely try to do so, a startup may not have the resources to service a large enterprise. For example, a multinational company with offices around the world will require support that's available 24/7 (you can't ask customers in Asia to call you in the middle of their night). And the bandwidth requirements of a large company may swamp the startup's servers.
But the biggest problem is stability: even if the startup's goal is to build a real business rather than being acquihired, most startups fail suddenly (e.g., due to cashflow problems and a lack of a bank credit line), and that would leave their customers scrambling to replace some critical part of their infrastructure. That's why established companies are reluctant to bet their business on a startup.
Anyone who is considering starting a company that markets to other companies needs to think about these issues (which probably accounts for the predominance of startups that sell to consumers rather than businesses).
If you are a startup offering 24/7 support, then staffing a 24/7 support desk needs to be part of your plan. It basically means cycling or dedicating two of your team members into the two 8 hour shifts that don't overlap with your primary operating hours. If you are getting a number of large enterprise signups, this should be easy to justify. These people could have useful roles (like QA) they are also performing.
But the biggest problem is stability: even if the startup's goal is to build a real business rather than being acquihired, most startups fail suddenly (e.g., due to cashflow problems and a lack of a bank credit line), and that would leave their customers scrambling to replace some critical part of their infrastructure. That's why established companies are reluctant to bet their business on a startup.
Anyone who is considering starting a company that markets to other companies needs to think about these issues (which probably accounts for the predominance of startups that sell to consumers rather than businesses).