I ask because I suppose it IS a fun side-game if I only had one character. Especially if I only had one character who had never actually hit the level cap yet. Because at that point you have an abundance of relics, shards, and IXP. You can put as much or as little time into your LIs as you want leveling up. And if you don't hit the current level cap before the next expansion is released, then it doesn't really matter. You will carry on as you have been.
However, this has been MY experience:
Mines of Moria: 5 characters who each needed AT LEAST 2 LIs each. There was no legacy extraction. What your LI ID'd with was what you got. *IDs and tosses literally 100s of LIs looking for those must-have legacies like Healing and Motivation Skills, Threat skills increase, Focus Bow Crit, etc* Carefully and lovingly maxxes out each legacy of each LI for every character. Grinds out top tier relics for all LIs. Finally got my perfect healing LIs for my Minstrel, now have to put together DPS LIs for soloing... Finally got my tanking LIs for my Guardian, now have to work on overpower LIs. Got my Gambler LIs for my burg, now have to make my Quiet Knife set...
Mirkwood comes along with a 5 level increase. What? My LIs don't grow with me? TRASH EVERYTHING AND START FROM SCRATCH. What do you mean I can't use Moria IXP runes with level 61+ LIs?!?!?! Become furious about unexpected LI changes. But continue to grind it out so I can still raid. Only able to get 4 toons instead of 5 raid-ready because it's such a grind. Secondary LI's get dropped for some classes (so long QK burg LIs).
Isengard comes along with a 10 level increase. Really? You want me to do this all again? *takes 9-month break from game because LI hamster wheel is too daunting* TRASH EVERYTHING AND START FROM SCRATCH. Only gets 3 characters casually raid-ready with LI's. Tiers not maxxed. Absolutely NO secondary LIs (minstrels don't ever need to DPS right?)
Rohan comes along with another 10 level increase. *takes 6-month break from game* TRASH EVERYTHING AND START FROM SCRATCH. Really wants to do group content, so gets 2 characters to cap and puts any old LIs in their hands. Purchases a few Scrolls of Delving, Scrolls of Empowerment. Grinds for T9 relics on 1 LI only. The rest will have to be 'good enough'. Decides to participate in a couple different leveling groups with lower-level characters instead of bringing up another 85. The socialization of a group and the great SoA/MoM content is much more fun to me than endlessly grinding LIs that will be thrown away every 10 levels.
Helm's Deep will come along in the fall with another dreaded 10 level increase. I have not decided if I will trash everything again, and put the bare minimum effort into new LIs (absolutely no scrolls of delving, empowerment, or anything. No grinding relics). Or maybe I'll just leave them with their 85 half-assed LIs.