Ok, I'll join the fun
The original poster purportedly asked a question about fuel management, but really he had already jumped to proposing possible solutions without having first clearly defined the problem. That's a classic pitfall in engineering. And most of the rest of this thread suffers from the same pitfall -- quibbling about the relative merits and risks of various proposed solutions, still not having clearly defined the problem they're trying to solve. No offense to anyone here. Just trying to boil this discussion down to its essentials.
So let's try to clearly define the problem. I think the fundamental question that underlies the original post is this:
"What is the most reliable way to access the last drop of usable fuel remaining, whether operationally and/or in terms of fuel system architecture?"
We'll call this
the problem.
It's a fair question to ask. Although, as others have pointed out, actually needing to use every last drop of usable fuel points to a more fundamental problem in one's fuel management practices. But let's put that aside for the moment and explore
the problem further.
If we had perfectly accurate fuel quantity indications in the cockpit, then the solution to
the problem would be trivial. We could run a tank to within drops/seconds of being "dry", then switch tanks with no hiccup in engine operation. However, in reality, we don't have perfectly accurate fuel quantity indications (neither the fuel gauges nor totalizer nor manual fuel burn estimates are perfectly accurate), so to prevent running a tank dry we have to switch tanks a little earlier, by the amount of uncertainty in the indications. So
the problem pertains to access to the last quantity of fuel that is equal to the quantity of uncertainty, i.e. the worst case inaccuracy of our best available fuel level indication in the cockpit. With a properly installed properly calibrated fuel totalizer for example, we're talking about a mere few tenths of a gallon. That's the quantity of fuel that this discussion is really all about, no more.
Now, in terms of fuel system design: To be able to access that last fraction of a gallon without fuel-starving the engine, you could add transfer pumps, etc. But as others have aptly pointed out, this adds complexity, both mechanically and operationally, and adds new failure modes and risks that likely outweigh its benefit. Now since we're talking fuel system design, a much simpler way to get that extra little bit of fuel, would be to simply make your tanks that extra little bit bigger, without changing the fuel system architecture in any way. Of course, no matter how big you make the tanks, someone will still ask the question, "how best do I get that last drop of usable fuel out of them"? And that's why this inevitably turns into a silly circular argument.
So I think it boils down to this:
It might make sense, under some
rare emergency situation, to actually deliberately run a tank dry and then switch to the other non-empty tank. But this is a trade-off between two risk scenarios that are both serious: One is the risk associated with running a tank dry and the consequent possibility of not being able to keep or get the engine running again. The other is the risk associated with forfeiting that last few tenths of a gallon in that tank, if (and that's a big "if") that last few tenths of a gallon would make the difference between making the airport or not. [Which of course, if that's the case, means you've already f***ed up big time.]
But under routine operation, i.e. a non-emergency situation, there is no good reason for your flight to be so fuel-critical that you need that last fraction of a gallon. And as such, there is no good reason to run a tank dry nor to alter the fuel system architecture by adding transfer pumps, etc. You simply need to plan and conduct your flight comfortably within your usable fuel capacity. And note that the legal minimums aren't necessarily sufficient minimums in practice under all circumstances. You have to use good judgment, taking into account all factors pertaining to the flight.
And a specific suggestion that I would propose, for those pilots that insist on flying at the edge of the envelope: Fly at the edge of a derated envelope. Aerodymaically and structurally, you already are, thanks to safety margins built in to the airframe specifications by the engineers. But they don't do this for your usable fuel indications. For flight planning and fuel management purposes, consider derating your usable fuel capacity by the amount of uncertainty/inaccuracy in your best available in-cockpit fuel quantity indications, whatever they are in your case. Doing this will ensure that you don't unexpectedly run a tank dry while your fuel remaining indication is greater than zero.