It will still be a measurable difference if you are watching hours of video, but for the gif replacement that this site suggests, it's negligible.
In general, encoding will cost you a whole lot more than decoding. Software encoders need to be really good to ship on the encoding side, and they're not there with AV1 yet.
Decoding, on the other hand, is pretty cheap. Hardware is still better, but it's been a long time since mobile CPUs were in a state that forced you to use a hardware decoder meet typical performance requirements. Bandwidth is so much more limited that using a software decoder to achieve a higher quality at a given bitrate is almost alway worth it.
Depending on the OS, if you watch a lot of video it is not unlikely that you are using a mobile app that uses, say, a software VP9 decoder.
It is not. Not with Modern Codec. Battery is so much more limited you will always want to trade high bandwidth than Software Decode. Apple tried VP9 software decode for youtube and all we got was very bad user experience. For most use case within a 20% bitrate, the difference between x264, VP9, x265 and AV1 are small, and you will always want to choose the one your user has hardware decode.
No one expect their Laptop , PC, Mobile, Tablet to get burning hot just watching a video for a few mixtures. Hardware decoding is literally the most important hardware on Mobile usage, and I argue the same for PC.
I think I pay about $10 a gigabyte? If I actually used that many gigabytes a month, the savings would pay for a new phone!
On desktop hardware support is not critical.
Just for comfort I prefer hardware decoding.