I am a TCA member and looked in several of their previous issues, but did find eBay listings much more informative re prices posted. I know that TCA is Lionel focused, but must assume I never learned "the secret TCA handshake...."
The TCA pub lists the entire MTH catalog numbers. Why don't they also list Lionel's?
If you mean the Buy and Sell list in the Headquarters News or the on-line equivalent (I don't know what else you might mean by "a few TCA catalogs" since the TCA doesn't put out "catalogs"), those numbers are filled out by the members themselves. It's not like someone at TCA reviews the content and confirms everything is accurate in terms of matching the number to the item description. (I've seen plenty over the years that just end up in the "Miscellaneous" section even though they are a very common item, and they may even have the item number in the description.)
As to why the "entire" number is or is not used:
1) since very early in MTH history, 20-# has meant Premier line and 30-# has meant Railking line. Since that's an important identifier, you really can't leave off the 20- or 30- if you want people to know for sure what you mean. I don't have examples, but I am pretty sure there would be a lot of overlap if you searched for things without the 20- or 30-.
2) For almost 50 years (until the change that drove the topic of this thread 2 years ago), nearly every item Lionel made in O Gauge technically started with "6-". Most things that did not were either other scale or maybe promotional items (Christmas ornaments, etc). With pretty much every item starting with 6-, it became very common to just list whatever was after the 6-, and people would know what you meant (the 6- added no useful information for 99.99% of the items). They are also listed in price guides without the "6-".