If a typical ML engineer makes $250K/year, she costs the company about $500K/year; that means the hourly rate should be at least $250/hr.
It's only a rule of thumb, it doesn't need to be exact, and the more you earn the less accurate it gets.
The less important part of the rule of thumb is for businesses to determine if it makes sense to have someone as a consultant or a full-time employee. But whoever is doing hiring should be able to figure that out for themselves because they should know how much the employee actually costs - but hey, even they might need help sometimes.
And that is the cheapest kind of firm with minimal overhead. For larger firms it is probably an even bigger multiplier.
For example in my country if I lose a job and I have a consultancy that I have made money on in the last year or two (I forget) you have to close it down, and then wait some months, and go through some bureaucratic thing to get them to say ok he really shut down the company before you can get the normal government payment for someone unemployed.
Obviously as starting a company is also not without its work and costs you don't want to do that, which means you need to have the money to last a few months between gigs.
Where does that £40k go? For a start we don't require private health insurance in the UK (we pay out of our taxes). Some of it is estates upkeep (offices, labs, capital equipment, cleaning etc), internal grants, support infrastructure (IT, computing), interview/acquisition cost, legal/HR costs, training, insurance, bonuses, employee benefits/pension matching and employer tax burden. Most universities put the rest into an "overheads" pot which can be used for a variety of things.
Most grants have a separate section for conference travel, publishing expenses, etc. In a smaller company, all of these things need to be added on (unless you're grant funded). So you're also considering expenses on top. If you pay someone to headhunt a candidate, that can be thousands plus a percentage of salary. We have access to a lot of training courses, most of which bill the university thousands per head.
The labour and legal costs alone of hiring candidates can also be very high. Think of a company like Google where your interviewers may well be on six figure salaries. In the US a typical hire costs about $4k. If your company depends on bums on seats to make money, the time between someone leaving and someone starting is costing you a fortune.
Depending where the company makes money, your overheads may also be paying for other staff. For example the university has an HR department, finance, legal, cleaning, estates, etc. None of those people generate any money for the university directly, though they are necessary for it to function. Some of their salaries are paid for by IP royalties, tuition fees and government subsidies, but a big chunk is from research grants.
Given all that, I feel like they are still just selling their skills for short term cash while others make the real money off what they produce. As always with contracting.