It's especially not cognitive-load building if you live at a hub (or a place with only one carrier).
Live in Pullman, WA? You're flying Alaska anyway.
Salt Lake City, UT? Get yourself a Delta number.
The tricky places are where there are lots of competing carriers. San Francisco with it's...pseudo-hubness for a number of airlines, Washington DC, etc.
Near Manchester, UK. Most of the flights I get are to the US, so BA or AA and I can use my BA number on both airlines.
That said, when I need to get a flight somewhere else and there's no BA or AA flight convenient I just get the flight I want to get and don't sweat the loss of status building.
SF is definitely a hub with about 50% market share to United. It's also a hub for the smaller Alaska (mostly via their acquisition of SFO-based Virgin America).
As a SFO-based frequent flyer, if you fly to numerous destination (instead of doing the same commute each trip), your choices are likely: fly United or take an extra connection.
SFO is weird, because it's a United hub, but there's just enough competition from Alaska nee Virgina America and Southwest that I could see being tempted off United.
Unlike say, Denver or Salt Lake for United and Delta respectively.
I'd also put SEA in this category, especially with Alaska and Delta no longer playing nice in the sandbox.
Live in Pullman, WA? You're flying Alaska anyway. Salt Lake City, UT? Get yourself a Delta number.
The tricky places are where there are lots of competing carriers. San Francisco with it's...pseudo-hubness for a number of airlines, Washington DC, etc.