This is a project with a 200+ year shelf life. Designing to 300 or less would have been short sighted, and many of the changes to accommodate such high speeds actually reduce costs in the long term (slab track, headroom to catch up delayed services, ability for one trainset to operate more services per day etc).
The cost overruns of HS2 are primarily from plain old poor project management, complex planning law and constant political meddling, not engineering decisions.