It can organise and control elements within the Regt and outside line Battalions. Once ongoing tasks are complete it can also coordinate Regt sized missions with lower delays than using an overloaded Bn HQ.
I tend to use Div and Regt HQ only for rear-area coordinations and for administrative moves ~ usually using Bn HQ to coordinate the local attacks/defences... but if more coordinated (rather than faster) and more powerful attacks are needed, then a higher HQ will be the better option.
If you have no more immediate & better use for 'LOC' troops they can be used to secure 'safe' rear-area objectives, freeing up front line troops for the front line or combat reserves... if you are doing this, do make sure that they have adequate local protection, for example from Gun Artillery deployed nearby, just in case enemy troops approach (which may the remnants from his FLOT or infiltrated small units, as well as the obvious 'major counterattack').
Units over a large area which are being used to secure point terrain features, or are part of the supply network, can be attached to a higher level HQ with 'defend in situ' orders and will reduce command delay while staying in their existing locations - it makes sense to remain as close to the organic grouping as possible to reduce command load, and to make future displacements easier to manage, with fewer detachments/re-attachments - it is also beneficial to keep Supply elements directly behind the supported troops (although at varying distances from the FLOT - Regt Forward, Division Intermediate, Corps and Army far to the rear, and artillery near to the supporting Supply echelon...)