Opening restaurants for breakfast

For many restaurants, the fixed assets (building, interior, kitchen equipment, etc) and the rent thereon make up a significant proportion of the cost base. Given that these costs are fixed, it would make sense to maximise the benefit from them, so why don't many restaurants open for breakfast?

Breakfast could be run by a separate shift of staff, and all that is necessary is for those staff to cover their staff costs, plus ingredients, plus energy, and anything more is profit on the existing setup. Synergies could be achieved if a good breakfast inspires customers to return for lunch or dinner. (Obviously the breakfast shift would need to leave the restaurant in a suitable condition for the lunch shift!)

There is no reason why breakfast needs to be that close to the normal restaurant in terms of genre of food, but obviously a complete clash could be detrimental.

To take this thought further, why not run the kitchen 24h, with the time while the restaurant is not open used to prepare foods to be boughts in an associated shop, e.g. fresh bread. Or alternatively, the kitchen used as the base for a takeout service.