Giving lame excuses - ‘we are understaffed’. Then hire more people. It’s not my fault you didn’t.
Who controls whether they can hire?
The company.
Not them. Not even their department, usually. The company. It's fair to politely point out that this is leading to unacceptable issues with service, and ideally, if possible you demonstrate this by no longer using that company, but there's no upside to attacking individual CS for this! All you're doing is making their day and probably yours worse!
And remember the calls are typically being recorded and/or overheard by supervisors, and if they hear the CS saying "They won't let us hire more staff" or otherwise implicitly or directly criticising the company, they're probably going to get in trouble or fired. So they aren't even allowed to be honest with you.
Lying to me - ‘I’ll call you back later when we’ve resolved the issue’ never calls.
This is a more real problem imo, because there are definitely companies where I've talked to them enough and understand their procedures enough to know when this is a lie or at least a wildly unrealistic gratuitous promise. And I don't think it's just procedure that it's used to get out of having to give a more specific commitment re: resolution. I've also seen within companies some real variance on how honest it is.
Like, with my ISP, I had terrible problems for six months, and I got pretty familiar with the CS. One of them would always tell you he'd call back or text, and absolutely never would. He was not unhelpful, and booked engineers and stuff, but would he call you? Would he pass on any information to the engineers? Absolutely not. Despite him being the one to keep suggesting he would! Whereas another one of their CS, she was absolutely on it, and always reliably contacted me and passed info on to the right teams.
Either way though, does it help to be rude or mean? No. Obstinate can sometimes be required, but needs judgement and you need to be politely obstinate and realistic in your asks and to listen to what they say.
Most organisations are pretty keen to send out "Was this employee useful?" surveys too - so if you really think someone is doing a bad job, well, there's your opportunity. If an organisation doesn't send those out? Guess what - they probably just don't care about the level of service you're getting! So...