"assuming that energy usage from a mobile browser is in the same order of magnitude as a desktop browser"
Any basis for this assumption?
Desktop processors are much less optimized for power consumption, and desktop browsers are also used differently with websites often time left running in the background tab, compared to the mobile phone.
I think the claim is accurate only because I've set the bar quite low (10x being an order of magnitude).
But I'll do a similar analysis: how much does a constantly-used desktop PC emit? I'm seeing estimates of ~200 kg emissions/year from a desktop PC for ~8hr/day usage, which is ~0.4% of the average American's emissions (50,000 kg/year). Now you must consider some other things:
1) of those relatively small emissions, how much is due to energy that is used for baseline PC functions (OS, monitor, etc).
2) does idle time from a browser doing slightly less work translate to noticeably less power draw? I can see a difference from 100% to 80% CPU utilization, but what about 40% to 20%? is the relationship between cpu utilization and power draw linear?
3) I'd bet the largest offenders of sites in terms of power usage are complex webapps that have no meaningful room for performance improvements possible by a frontend developer: games, photo editors, video players. Compare to those, better CSS selectors seems small potatoes.
To be clear, my claim is that overall the savings here are negligible and efforts are far best spent elsewhere (extreme example: instead of a programmer trying to optimize even a heavily-trafficked site, they would have a larger impact if they spent their time ensuring their home, or the home of their friends and family, is not wasting energy).
Any basis for this assumption?
Desktop processors are much less optimized for power consumption, and desktop browsers are also used differently with websites often time left running in the background tab, compared to the mobile phone.