It depends– if you're trying to run a specific algorithm on your new supercomputer, then you'd almost certainly be better off paying for researchers to optimize or improve on that algorithm.
If that's the situation (which it is for e.g. weather forecasting or computational fluid dynamics), then a billion pound supercomputer is likely to be more of a boondoggle than a sharp-eyed investment.
A good implementation on a desktop can beat a bad one running on a supercomputer.
But if it's a time-sharing system, then it might not matter as much.
The supercomputer at my university tends to run a lot of one-off jobs like an experiment repeated thousands of times with different parameters.
On a desktop that might take weeks, but if run in parallel it's like a couple hours.
Tightly optimized code might bring that down to an hour on the cluster (or a mere week on my home PC) but I wouldn't bother because making the code more efficient might itself take a week or more.
So the fastest way to get the results I need would be to just run it on the supercomputer.
But if it's a time-sharing system, then it might not matter as much. The supercomputer at my university tends to run a lot of one-off jobs like an experiment repeated thousands of times with different parameters. On a desktop that might take weeks, but if run in parallel it's like a couple hours. Tightly optimized code might bring that down to an hour on the cluster (or a mere week on my home PC) but I wouldn't bother because making the code more efficient might itself take a week or more. So the fastest way to get the results I need would be to just run it on the supercomputer.