No.
If you cannot self-rescue, someone will notice your absence and SAR will eventually be deployed. Leaving behind your inReach requires a full search, which wastes valuable SAR resources and possibly even puts SAR professionals at additional unnecessary risk. If the emergent event is the result of something that impacts a large area -- storms, earthquakes, avalanche, rock fall, etc. -- other people may die because SAR spent too much time on you.
If there is ANY chance that SAR will be deployed to help you -- requested by you or otherwise! -- it is incumbent upon you to either carry an inReach or give regional SAR an explicit "do not rescue" request prior to departure.
Frankly, that’s silly.
In the very unlikely event that something goes seriously wrong, having a satellite-based emergency beacon is easily the difference between life and death or serious life-long injury.
I’ve spent plenty of time in the backcountry where cell service is not just spotty, but nonexistent. Now that beacons are cheap and widely available, I always take one.
Being self-sufficient and disconnected are good, healthy experiences — having an emergency communication mechanism for emergencies that you cannot handle yourself doesn’t detract from that.
And if their response is "that is stupid, take your sat device" then do so.
Tangent, but it is interesting to me, how many people now seem to be unwilling to go out of cell range. It reminds me of people decades ago who would go camping, but only with a car. If you had to leave powered-travel range, they were out.
This is less the case for me now, but there was a time when leaving my cell at home was a huge luxury. And I still enjoy days when I can go do things without it - pretty much the only time anymore when my time is truly my own.