It is not an elliptical or shortened version of would like to. It is rather a different, older sense of will meaning be willing to.
The modal auxiliary verb will developed from an Old English lexical verb which meant approximately want, desire. Today the modal has three distinct senses:
futurive, signifying future time reference
Tomorrow John will go to London.
John said yesterday that he would finish the job when he finds time.
dynamic, signifying persistent action
When I was a child I would often read for hours every day.
If you will keep teasing her you must expect her to get angry. (In this use, where it means approximately "If you insist on teasing her", will is strongly stressed.)
volitive, signifying willingness
If they would only listen they might learn something.
If you will bring beer, I will bring chips.
The dynamic and volitive uses may include future reference.
Tom is the best expert ...
Assertion of a fact. Where there are agreed criteria then there's no need to hedge an statement.
Djokavic is the current number one male tennis player in the world
When criteria are less certain, or we ourselves are not sure of our facts, or we wish to be modest by appearing to be uncertain of our facts we may use I think
I think Djokavic is the best male tennis played of all time
I think that the population of the UK is 50 million (actually 65 million)
This formulation implies that we are open to correction and discussion
Adding would softens this further, emphasises that we are uncertain
I would think that the population of the UK is greater than 50 million
The I would have thought formulation is normally used in a context where some information has recently been given. Depending upon the context it may imply that we are actually contradicting the information, or that we are expressing surprised acceptance.
I think Tendulakar is the best batsman of all time
I would have thought Bradman had a better record
that was disagreeing, suggesting that by some criteria Bradman is better
The current UK population is 65 million
Oh, I would have thought it was only 50 million
but now I've changed my opinion (this implied but not said)
that was agreeing, I thought it was 50 million, but I accept your statement of 60 million is correct. We could just say
Oh, I thought it was only 50 million
With pretty much the same meaning, the slight difference being that the second case implies it was actively in my mind, whereas the would form could imply that I hadn't really formed a solid opinion until now, but I would probably have guessed 50 million.
As your comment indicates we are indeed into shades of meaning and idioms. In these cases the tone of voice will often differentiate the meaning.
I would have thought Bradman had a better record
Would probably said with a questioning or challenging tone and raised eyebrow.
Best Answer
Below I rewrite your sentences slightly to emphasize their differences. I replace 'thought' in your second sentence with 'did think' to make what I have to say more obvious.
Note the brackets around the differences. Either sentence would work; they have similar meaning. Both sentences are the speaker justifying his decision. In the first sentence the negative word used is the 'not' inside "didn't" (did not), while in the second sentence the negative word is the 'not' inside "couldn't" (could not).