You can have this same problem in reverse - where a race has a 'gun' start and chip finish and then someone starts late and throws a fit because their 'Garmin' shows them beating the overall winner or an age group winner. People management, providing education on how timing works, and diffusing someone's frustration is just part of the job unfortunately.
If you capture chip start times when it's not necessary then I would imagine you'd have more problems with this than if you did a simple gun start with a chip finish, because obviously it's more likely that people would notice that the results on paper do not match what they perceived happened at the finish line. Imagine being proud of yourself for gutting it out with another participant and finishing ahead of them and then the printed results show them finishing 20 seconds ahead of you. Your typical 'couch to 5K' participant thinks you made a mistake. When the race is small and there is no chip system at the start, most participants intuitively know that results are bases on the actual finish order. So you're much less likely to have complaints.
We don't ask or offer to provide a chip start time unless we feel the race is large enough to justify it. Typically 400+ athletes is where we'd start to consider it. Most race directors wouldn't think to ask for a "chip start time", but I'm sure that nearly 100% of them would say they wanted it if we gave them the option for it, whether or not it makes sense for their race or not. Often they're just as clueless as the participants when it comes to knowing net time vs gun time. If the start and finish is at the exact same location then we may do it just for the heck of it, primarily so that we have both times and so that we have a good idea of which athletes are actually on the course.
If you're going to offer it, then here are some recommendations:
1. It MUST be the race director decision!
2. If someone challenges you on it, make it clear that this race decided to base results on 'chip' time so that is what you did. Give a short explanation of what that means of course. If they're still upset, tell them to take it up with the race director.
3. If the race director catches grief over it, they can politely point out that the rules for this race was that results would be based on 'chip' time. When they signed up for the race, they signed up to follow the rules of the race.