Well, for one, many organisations limit coaching to line managers, but that shouldn't be the case. All managers should be enjoined to coach their subordinates. It should be a management style, rather than an activity.
I agree. Coaching should be ingrained in everyone in the organisation for it to become a culture of sorts. At our office, we encourage all managers to coach their teams and even people who belong to other teams. We incorporated these into their performance evaluations.
As HR practitioners, we also have the responsibility to make sure that the coaching is done fruitfully, and you should assess the quality of coaching that goes on. If this is not enough, you might want to hire external coaches to augment the coaching done internally.
Coaching is a cost effective way to develop your employees' talents and skills. And coaching or the ability to coach should be developed in just about anybody in the organisation, BUT it should be a vital skill for those in supervisory and managerial positions.