I think the point of the admin-focussed bits of HR is that they do all the stuff that line managers can't or won't do. Consultants are after all notoriously bad/uninterested at anything approaching operational management, so HR admin have a role there in terms of keeping things ticking over, making sure you're paid, bonused, benefited etc. And after all, if they didn't chase us for performance management then it'd never get done and bonuses would go back to the bad old days of "discretionary" reward.
It's not just in consulting that people get frustrated with HR - in industry too, operational managers often complain that the HR policies don't match the reality of the business they are in. In industry, one of the answers is to employ HR business partners who work alongside managers to get the strategic side of HR and people development working. In consulting, we are still behind the times in that respect as few firms use business partners or have very sophisticated HR policies. Consulting partners tend to be opposed to anything that would mean ceding influence within the organisation on that kind of level, and the business model tends to rely on the luxury of so many good people applying that they can afford a high burn rate of staff and low efficiencies in hiring and staff development.
In short, HR in consulting tends to be focussed on the admin side of things even more than usual. My experience is that HR admin is no worse than admin in other functions e.g. purchase and sales ledger within finance, or IT, or procurement, for example. However, they come into contact with other staff and have a much more public role (e.g. for recruiting) so the cracks are more visible.