What does the adenosine do in ATP?
The adenosine part is needed to make DNA and RNA.  It is logical for the triphospate to be attached to ADP, GDP, UDP or CDP since they are needed to make DNA and RNA.  

In some instances, GTP is used instead of ATP.  In fact the Krebs cycle does involve phosphorylation of GDP.   GTP is used in the formation of microtubes by tubulin.

I've seen some give the rate of hydrolysis being greater for ATP than GTP as a reason for ATP being more utilized.  

There is a related question here: https://biology.stackexchange.com/questions/11286/why-is-atp-the-preferred-choice-for-energy-carriers