I'd say it depends on situation. Providing Personal Security Details (PSDs) is a job performed almost routinely by even Tier-1 operators in US like Delta.
Gen. Norman Schwarzkopf (their COAS during Gulf Wars):
Delta (as well as other units from JSOC) still does PSD for important personages (including Chiefs of Staff) around the world depending on threat perception.
Thing is, its very difficult to source top-grade operators who're in their prime from anywhere except SF. Either they need to be deputed from SF into a specialist cell with PSD role, or just assigned from within their current Btn to this role. Latter is simpler, but either way its a drain on same resource pool so doesn't matter.
That, or you need to create & maintain a new sub-organization within MP like SPG dedicated for raising & training a cadre specifically for this role. Regular MPs who's job profile includes arresting drunken solider from canteen just aren't fit for this task.
But creating a new resource pool is a very expensive proposition and I very much doubt MoD would sign off on such budgets - Plus, to them creating SPG-type org for military would seem like making Generals on par with elected representatives of top office.
Democratically elected leaders, whether Indian or American, are always queasy with such a proposition.