It has a cumulative effect and drives the continual "upgrade" cycle. When you consider the life-time of an average mobile device, and the resources required to manufacture and ship them, it's a not insignificant problem.
>Berners-Lee writes that in 2020, there were 7.7 billion mobile phones in use, with a footprint of roughly 580 million tonnes of CO2e. This equates to approximately 1% of all global emissions
Of course, not everyone is replacing their phones yearly. Another source[2] says the average consumer phone is 3 years old. That works out to 0.33% of global emissions, assuming the phones aren't recycled/reused to developing countries. Even if assume people are upgrading their phones for app/web performance reasons, the impact is far less than 1%.
[1] https://reboxed.co/blogs/outsidethebox/the-carbon-footprint-...
[2] https://www.statista.com/statistics/619788/average-smartphon...
It's still somewhat surprising that one could attribute 0.2% of global emissions solely to phone power consumption... I would have expected it to be lower.
Having gotten away from 500+ watt desktops as the standard for light non-gaming computing has been a win in the energy consumption court.
I think there are lots of good reasons to avoid the upgrade cycle but energy consumption of the end device itself probably isn't it. (Embodied energy of the devices, environmental impacts of mining, no good EOL story for ewaste, etc)