I would like to see the speech skill get more useful in different circumstances.

For instance, why do all bandits, forsworn and other non-monsters instantly attack you upon sight. Here it would be cool to maybe talk yourself out of trouble, maybe start some radiant quest.

Like highwaymen that actually just wanna robb you and not just kill you... they demand a certain sum of money or favor... which if you don't have will result in a "you have a week to give it to us or we'll find you again" or "we'll take all your money untill you kill our rivals"

All these could be dependent on your speech skill... if you're good at it you might be able to talk your way out of these... if you're average at speech you might get two weeks for instance... if you're really bad at speech... well maybe they'd kill you right away or just take all your money with no possibility to get it back without bloodshed.

These are just a few examples of how to "enrich" the use of the speech skill.

Also this would be very useful if you for instance wanted to RP like a merchant or other non fighting class.

Speaking of non fighters i feel that Skyrim being an fantasy RPG is lacking alot in alternatives. How cool wouldn't it be to be a traveling merchant with your own caravan of guards and servants... or a traveling bard who actually COULD sing and/or play instruments.

Merchants could use their sharp tounge instead of swords... and on enemies they instead could rally fighters and NPC's to their cause.
Bards could use their wit and words to soothe villians or theis affinity to flatter to rally NPC's to their cause.

There are so many non fighting/sneaking/casting events and experiences that is lost due to this lack of speech craft.

heh I just thought of Morrowind, where if you could get your Personality up to 100 even hostile people wouldn't attack you

The speech system in Skyrim is reminiscent of Fallout 3 but is nowhere as good as Fallout 3. Hopefully, when the official editor becomes available, we will be able to fix these flaws.