Computer keyboards grew out of calculator key assignments, as both are business tools.

The telephone keypad arrangement was derivated in an UI analysis in 1959/60 with 'average' customers - people at the time not really in contact with calculators or even less computers. //

In 1959 Bell did a rather large UI study, published in 1960 as "Human Factors Engineering Studies of the Design and Use of Pushbutton Telephone Sets". Goal was to determinate a layout that would not only work, but as well operate efficient and be enjoyed by users. //

One might speculate that if calculators would have been more wide spread in the 1950 (they were special and expensive business tools at the time) or terminals/computers had already made their way into homes before, the telephone would also work bottom-up ... but that's fooder for alternate history novellas.