“What happens if I don't get a bone graft after tooth extraction?”

The potential consequence of not having a socket preservation procedure done at the time of the extraction is that you may not have enough bone height and width to have an implant placed at a later date. If there is not enough bone for implant placement, extensive grafting procedures would be required or you may have to consider a fixed bridge or removable partial.

Bone graft preserves bone contour to make an implant or bridge pontic fit better. They are done more simply at time of extraction and more complex and cost more in later years after an extraction without one.
Hope this is helpful.

Bone grafts preserve bone height after extraction which is extremely important, especially if you are planning on restoring the area with an implant. The area will heal without a bone graft but there will be concave defect area that may disqualify you from getting an implant. Not a big deal if you decide to have a traditional bridge to restore the missing tooth. My suggestion is to get the bone graft if you are not sure how you are going to restore the missing area. It will save you a lot of expense if you do it at the time of the extraction versus afterwards.