Correct me if I'm wrong with any of these but this is what I believe to be the case as of now:
For the first raid tier, maximum item level any item can be bumped to is 895 [source].
The maximum item level in the database is currently different depending on the item in question (900 to 955 depending on the item, e.g. 955, 940, 930, 900, etc.).
Now if you wanted to, for example, look at which would be the best trinket in the first raid tier (so 895 max), it'd be really hard to determine that with the current list format because it has lots of trinkets at 900+. Arguably even more importantly, different trinkets are included with different maximum ilevels (even though they'd have the same maximum ilevel ingame) making it hard to just look at each trinket's top occurrance and assume that all trinkets scale down roughly linearly.
While showing item level would obviously still show you the trinkets not available in the first raid tier, a simple CTRL+F search for 895 (or your desired item level) could let you easily compare all trinkets at that ilevel and manually filter out the ones in the second raid tier (if so desired).
Of course there might be other solutions to this issue as well but I figured adding the item level might be the easiest since it's certainly used within Simulationcraft and is available in the XML of the wowhead links you've added.
Edit:
In case anybody else finds it useful, here are the lists showing item levels as well:
BM
MM
SV
Item levels were extracted from the respective wowhead XML pages using a simple python script. If you see any errors, feel free to point them out.