Though it might not be that important for practical tune-up (where, as you say, you can use the rig's SWR meter), I'd really like to get some confirmation that my antenna is somewhere near 50 ohms before letting my transmitter touch the antenna. Also I like the idea of tuning up without causing QRM, however brief.
Modern transmitters have high-VSWR-foldback circuits that reduce drive proportionally to SWR. What will
kill a solid-state rig is overtemperature, which can be caused by endless twiddling trying to achieve perfect 1:1 SWR at too-high power levels. PA modules have built-in temperature sensors, but modern rigs generally have inadequate heat sinks, to save weight and cost. The PA transistors may sacrifice themselves to save the sensors. AM rigs were designed for 100% duty cycle. Not so the rigs of today.
Believe me, with that antenna, the few tens of mW needed to measure SWR aren't going to cause QRM!
But if you can find the components, by all means build a noise bridge. They're fun to play with.