The Arup routing for the Channel Tunnel Rail Link meant lots of tunnelling. As far as I understand it, the route always planned for a big station box at Stratford as this would break up the two long London tunnels and provide a link for the depot at Temple Mills.
Long tunnels cause problems for fire protection, as the intention is for a train with a fire on board to continue running until clear of the tunnel rather than stopping within it where smoke and access is much more of a problem. The relevant rules for high speed infrastructure in Europe mean that any tunnels longer than 20km have to have special measures to protect against fire. The Channel Tunnel has the service tunnel for evacuation and the Gotthard Base Tunnel has two intermediate emergency stations (Sedrun and Faido) at about 20km intervals along its 57km length. These regulations also make it hard to extend the HS2 tunnels much further into the Chilterns.
Couple this with the need to have intermediate tunnelling points, and track crossovers, and it makes a lot of sense to build one of these big boxes along your route in a convenient location. We've known for a long time that the railway lands at Stratford would be suitable for major regeneration. The Olympics made it more important, but it would have still been a useful area to have a station. The concept for Crossrail since the 1930s has been to link together the Great Western and Great Eastern networks, which makes Stratford particularly useful as an outer interchange point for London.
The extra cost involved in putting a station in the box wouldn't have been that high. You'd need some sort of platforms and some emergency access lifts and stairs down to that level anyway. One of the use cases the station was meant to have was as a London stop for north of London Eurostar services which would turn onto the NLL near King's Cross and then the WCML rather than going down into St Pancras. These haven't ever happened, and it hasn't ever made financial sense to slow down Eurostar services. The need to use the station for the Olympics Javelin service was probably enough to make the small cost of the station worthwhile in the end.