I was under the impression the situation was opposite to this; Richard was firmly opposed to pushing on to Jerusalem, while the bulk of Crusaders wanted to attack Jerusalem.
It's a bit more comples : in October 1191, Richard did went to Jerusalem with a large opposition (don't forget that not only local latin lords represented a large part of the Crusader forces, but that French crusaders were more or less scattered around Acre at this point).
In May 1192, tough, it was the exact contrary : most of Latin and Crusaders wanted Richard to go to Jerusalem, but Richard refused (in no small part because they proved to be unreliable, but also because he alredy commited most of his forces to the ongoing campaign)
Hence why he resigned command during the second march to Jerusalem, in protest at marching to attack a city that he believed they either wouldn't be able to take, or wouldn't be able to hold once taken.
If we read the "official" chronicle of Richard's Crusade, made by Ambroise, this is rather the mind set of Crusaders and Latins that didn't joined up with Richard, fearing that the campaign to Jerusalem would proove perillous and that even if the city was taken, they wouldn't be able to hold it : for them it was too risky to bet everything on the capture of Jerusalem.
The refusal of Richard in 1192 is a bit more complex t : his main argument was that he didn't want to go trough a campaign that would be blamed on him eventually. His strategical refusal was less due to the state of the city of Jerusalem, than that for him Saladin could follow the Crusader army very easily and that he knew their situations, their strength and their weakness, with Saladin eventually cutting their supplies down if they went to Ramla. Not that he didn't mentioned the strength of Jerusalem (which was frankly really relative).
And Richard didn't wasted an opportunity to say "and if the expedition would go wrong, I know that French (french crusaders that wanted him to besiege Jerusalem) would be the first to blame him.
And it wasn't the case that the Crusaders at this point had no chance of taking Jerusalem - Saladin was in the process of evacuating the city when the second march to Jerusalem turned back, which is normally taken as suggesting that Saladin believed the city would fall to a Crusader attack.
Which wasn't much the point of the Latins that refused to go in Jerusalem : rather they were certain that they couldn't hold the city without much supplies (due to Saladin's scorched earth tactics) against an unavoidable Ayyubid attack.
That said
@RogueTraderEnthusiast , I did found one occurence to the idea to attack Egypt. I'll translate it a bit there (as I don't think most people there are familiar with Old French)
But to people that are from this land
That want to recover their fiefs
Them we must follow
And the advice of Templars
With the agreement of Hospitalers
And people that before went
Into this land and knew it
And still know it
To them I'd want
we'd let to decide
or such siege to do
or to go take Babylone [Egypt]
or Beirut, or Damas
Then we would not disagree
While people disagree now
There, we have the usual proposition of a council : let's remember that while military matters were extremely commonly made trough a council everywhere in feudal Europe, it did have a more formal and institutional role within the Yerosolemite Kingdom. Richard cheats a bit, because he refuse to listen to French crusader, and most of Montferrat's local support aren't there. Hence why he does turns to Templars and Hospitaleers, which are present (altough in small numbers) and more closely tied to Richard's side.
You'd notice as well that taking Egypt is just another proposal between Jerusalem, Beyrut, Damas.
Here's what follows immediatly
From Templars there was five or four
to get rid of problems (not sure about this one)
And as much Hospitalers
And Syrian knights
And as much French barons
They were certainly as many as twenty
Oaths were taken by all
On they loyalty to agree
To do as decided
And they decided and said
that great good fighters of the land (not sure about this one)
had to conquer Babylone
And when Frenchmen heard this
They were so enraged that they broke their oath
And said that they will go to the siege [of Jerusalem]
And that they would not go anywhere else
When the king about the discord
That God didn't want to resolve
Heard it was because of the Frenchmen
Certainly said this to them
That if Frenchmen had trusted him
They would be in land of Babylone
"As I did prepared
To carry supplies
And biscuits, and wheat
To be carried trough sea
And I would have lead with my deneers
In the name of God 700 knights
And 2000 seargents
I would have led with them
Must be know to them
That to no brave man
I would have lacked support
I am entierly ready to go to the siege (again, of Jerusalem)
If, by St. Lambert of Liege
they know I won't lead them
But go in their company
Sorry for the length, but I think it's best to have all the context we need. Let's gather our informations.
- Ambroise suddenly mentions a plan by Richard that wasn't mentioned and will not be from this point onwards. Not only this, but it's mixed with other proposals and only appears as Richard is hard pressed to go to Jerusalem by a significant part of Latins. It's not really unthinkable to consider he might just have planned...something to prevent being forced to lead an expedition to Jerusalem (as the last translated sentence highlights IMO).
- Richard have as many 700 knights and 2000 sergents ready to go to Egypt, plus a part of Crusaders (not all, as it's apparent French crusaders simply won't go, as well as Montferrat's supports). Let's say at best 8,000 men. Is this really enough to not only conquer the Delta, but push back Saladin's reinforcements from Syria?
- If Richard really had the means and the will to attack Egypt, he would have done so after Arsuf, IMO, when Saladin had to retreat and to resort to general destruction : instead he did took time to rebuild Syrian places and even to go to Jerusalem against the general advice. It seems that he had no such plan before 1192 when it was clearly too late, regardless of the genuity of the plan.