If Alphabet wanted to prove they lasted three years, they would have found a way to prove it. Auditors don't go around challenging on things like this. In particular, they don't go around challenging companies on depreciation because that is a key lever that management can pull if they need to hit numbers.
It is very difficult to discern exactly why they will have done this but the functional answer is: they have done this because they needed earnings to increase. In this case, it looks like the difference between a 15% and a 20% beat (I believe the change was made in January, I think they had quite a big beat in that quarter after some flattish momentum, middle of the year very strong anyway).
I worked in audit for several years and the auditors will challenge any estimate made by management that the auditors deem material to the financial statement readers. And the useful life of how long computers last is an estimate by management. While at most companies useful lives might not be an estimate worth looking at, Alphabet has enough computers for this to be a material estimate (likely due to GCP) that is subject to management bias. The public auditors are there to ensure (to a reasonable extent) that management can't manage earnings by changing estimates like this.