You can just prepend the object name to the calls...
As far as I can tell, VBScript supports with statements, I tend not to use them. I tried it out really quick, and it seems to work. I don't like how in VBScript you end up with a bunch of "call .something" in the code. To me it looks like a typo or something is missing.
It's language specific, not tool specific. "With" statements are part of the Delphi and Java programming languages which you are allowed to use, in their script form, in TestComplete. So, it's not a matter of why they chose to include that logic, it's a matter of picking a coding language that will meet your needs.