Whether you should buy an umbrella depends on your personal risk tolerance. I have <$100k of exposed assets (my home is completely protected under my state's law), most of my money is in ERISA-protected accounts, and I feel comfortable with my $300k limits.
First off, from a personal insurance perspective, the bulk of the exposure to liability is from driving. That's probably why the OP couldn't get an umbrella over their renters insurance, because the insurance company relies on the auto pricing to get to their premium. They can't even calculate how to charge without it. Which is why the first step I would recommend is to get an Auto policy if you have a driver's license, and get a $300k or $500k limit there.
Second, I think it's important to understand how "profitable" is determined in the insurance industry. When you or I are determining whether our insurance has been "worth it", we look at how much we've been paid (losses) compared to how much we paid the insurance company (premium). The insurance company looks at that too; they call it the "loss ratio", losses divided by premium. They also look at their business expenses and get an "expense ratio" by dividing total expenses by premiums collected. Loss ratio plus expense ratio equals "combined ratio". If the combined ratio is under 100%, the insurance company made money, if it's over 100%, they lost money*.
The industry average for auto loss ratio has been between 70-80% for the past 10 years. Industry average expense ratio has been 25-35% over the same time, for a combined ratio of 95%-115%. The industry lost money on auto for most of that time, partially because they didn't adequately account for the impact of smartphones on accident rates, and the <100% combineds are pretty new.
In contrast, umbrella loss ratios have been 30-35%, and expense ratios are 30-40%, leading to industry combineds of 60-75%. That's what I mean when I say that it's insanely profitable.
So, yeah, it's really cheap peace of mind. No argument. But what you could actually expect as your fraction of the overall risk is about a third of that premium.
The final thing that I think a lot of people don't realize is how personal liability claims typically work. If your average John and Jane get into an accident, even assuming they're both insured, they likely don't have limits over $50k, which doesn't go far towards medical bills. Let's say that police assigned fault to John, and Jane has injuries well over John's limit. Jane can certainly sue John, but every attorney she's going to talk to is going to say "yeah, he's definitely at fault, but you can't get blood from a stone, so it's not going to be financially worth a suit". Attorneys often say that without even doing any research into John's actual assets; they'll judge based on his job title, the kind of car he was driving and the neighborhood he lives in.
A mustachian, driving a below-average car, with an unremarkable job and modest house, is not going to smell like profit to anyone involved, and if you already have an insurance limit that's many times the average and well above the legal requirements, in my opinion you've gone above what can reasonably be expected to compensate someone you're liable to.
However, maybe your risk tolerance for stuff like this is low, or maybe you're not as "stealth" with your wealth as many on here, or your job is one generally assumed to be well-paid. If that's the case, please contact an independent insurance agent to buy your insurance. These are experts who can help you find an insurance company to meet your needs (maybe there's someone out there writing $1M liability limits on renters policies?). I've been with mine for forever, and have never been able to find a better price, because they put me with a company that has a specialty coverage for "leisure" vehicles (driven <7500 miles/year and not used for commuting).
*Or, they lost money before investment income was accounted for, but that gets too complicated for our purposes here.