In the mean time I did also used pngcrush on mines to recompress and get rid of photoshop metadata and I did also reduced them significantly. Most are actually <10KB... total 2.5MB of 251 picons... anyway no change at all. Btw, these are my picons: Zippyshare.com - nos_cabo_220x132_nologo.rar
Honestly I don't really think it is in any way related to file size... note that I said I get problem even with local kodi running on same RPi2 as tvheadend (as well as in a remote RPi connecting to that same tvheadend) BUT no problem at all with Kodi running on Windows PC and connecting to the same tvheadend on the RPi2...
In the mean time I did also setup a RPi3 for a friend and again re-did some few tests with this with a completely clean Libreelec... and I did even test it with tvheadend42 also running on that new RPi3... same exact problem!
One thing that I should say is that once picons are cached on kodi (after long time waiting to fetch them all) then they allways show ok, but if I clean icons cache on tvheadend (that causes icon number to change on the /imagecache/nnn urls) then kodi will also need to fetch them all again and same delays and timeouts appens again.
I'm really surprised that no one else reports same problem... I'm having it since OE6 at least, did clean installs etc and can always reproduce it.
Besuz: In your case are you running Libreleec (with tvheadend) on a RPi? (I ask it as I can't reproduce it on kodi running on Windows then it may be either RPi or Linux specific, not sure) and in your tvheadend in Configuration -> General -> picons path, you have it set as file:///storage/folder_with_your_picons... or and http url to a 3rd party http server with the picons?
Thanks for your reply.