There has to be some sense of proportion in these things, we are about ready to replace our second most popular page (after the homepage the page with the highest page views) primarily because Adwords says "below average" Landing page experience!
It might still make sense to replace that page because it could better be reinvented as 4 separate and more focussed pages, but I am not sure "Below Average landing page relevance" should be the primary guide of which pages get the chop.
Keep in mind that LPE is keyword specific, meaning if you aim wide, into an area where the keyword is not very relevant to what;s on the landing page, you LPE scores for those keywords could be low.
Meaning, before you go changing up the landing pages, dig thru the data and decide if the page has issues, or if some keywords you're sending there are the issue.
Like let's say you're using Broad match keywords, few Negs, and you're dragging in all kinds of widely aimed (shotgun) searches, and you're pointing them to a landing page that is specific, and the content / products are limited in scope... your keyword and ad practices might make the landing page a poor fit for THAT traffic.
I used to take it for granted that my peers (all of you!) spent as much time as I do, digging into the Search Terms report. :-)
But perhaps 25% of PPC Keywords Jockeys take the time to do this critical work.
The other 75% let their horses run free.
Pick a keyword or three with a poor LPE score, do a Search Terms report on each keyword, then ponder on the degree of relevance between those Searches, your Ad that is triggered, and the Landing Page the traffic is sent to.
Earlier I was saying the QS points, really are #1 and #2-5.
Make sure your research on #1 is thorough first.