Pretty much yea, though I'm sure it's not unheard of for people to lend objectives out whilst others are getting their stuff together (thanks Mephiston

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For myself, I think they're just a neat tiny little project to add a bit more flavour to your army.. like my objectives are representative of objectives marines would go after: the fallen comrade by the broken vehicle... perhaps he was carrying some once lost chapter artefact when he was ambushed and the marine force is out to retrieve his body and the artefact? similarly, the fallen statue could again mark some important artefact, or it could mark the site of a famous engagement / victory of the chapter?
Orks... might have some looted 'teknology' that the orks are keen to get their hands on, maybe it'll make their guns more shootier / more bangier?
Chaos... some long forgotten artefact from the fall of the eldar has been uncovered and the chaos forces are out to recover it for their own nefarious purposes?
Just nose around your army's fluff, instant inspiration

I've always assumed that objective markers had zero impact on LOS nor do they provide cover, whether you put the objective marker
in cover is another matter altogether though
