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We're building a motor-drive circuit using an L6206 dual H-bridge circuit. The bottom side of its H drivers come out of a pin called $V_sense$, intended to be connected to ground or to a low-side current-sense circuit. I'm expecting to drive motors with PWM up to an amp or two.

I want a logic sense line to indicate whether there's any current flowing (say $>10mA$), or not. It's essentially detecting the operating presence of the (removable) motor.

I think I can do this by comparing the voltage drop across a Schottky diode with an approx $0.25V$ reference. I'm thinking of using a divider to create a weak $0.25V$ voltage source from my $5V$ power supply, a $2A$ Schottky diode (eg SB240, $V_f=0.5V$ at $2A$) with a small $25Omega$ bypass resistor to eat any leakage, and a comparator (eg LM324 op-amp, or LM339) to create the $5V$ logic result.

^{simulate this circuit – Schematic created using CircuitLab}

Wherever I have looked up designing current sense circuits, there is always a low-value power resistor to create the voltage drop. I haven't found any that use a diode. I think that a Schottky diode is perfect: its voltage drop will clamp off nicely so it won't waste heat, it's cheap and simple.

Perhaps everyone else is interested in measuring the current level, where I just want to know if there is a current at all? Or, they only care about being close to a maximum current, where I want a minimum?

Why don't I see any diode-based current sensors?

Note: my logic output essentially goes into a latch, so I don't care that the signal will flap around with the PWM.

You can choose the resistor so that it consumes the same power, or less if you want to. At 2 A the diode will consume 1 W, so "equal" resistor would be 0.25 Ω. At smaller current, say 1 A, the diode will consume roughly 0.5 W because the voltage doesn't drop that much. There the resistor only consumes 0.25 W, which is significantly less.

The diode is not accurate. Its $V_f$ varies especially with temperature. Junction to ambient thermal resistance is 45°C so you can expect that much heating with the maximum current. And if you have some heating from outside (direct sunlight for example) you can easily reach 100°C temperature for the junction which drops $V_f$ to half from the original. A decent resistor drifts something like 50 ppm/°C, so at temperature rise from 25°C to 100°C the resistance changes only 0.375%

With a resistor you do need an amplifier, because at low current the voltage is also low. But there are circuits made for just that, so implementation is not difficult. Search for e.g. current sense amplifier. Some of those even have a built in comparator so the number of components might even be the same as with the diode + comparator solution. And while you are adding an amplifier, you can drop the resistor size, and get away with a lot less power loss than with the diode.

So the answer to your question is, diode based solutions are not accurate, and consumer more power compared to shunt resistor solutions.

Change the idea. You can insert an active low current pulse circuit to detect if there's a load connected. If the voltage depends enough on the pulses, there's no load.