Elfwine said:
Point taken on the conditions of the siege, but will Richard really have more time, or will Philip just leave earlier (and thus give Richard the same grief back home)?
I don't think Philip would leave the Crusade earlier with no siege at Acre. But I think he could still leave later in the campaign.
OTL, Philip Augustus left the crusades for several reasons :
1°) He had a huge quarrel with Richard.
First, on their way to the Holy Land, Richard cancelled his engagement to Philip's sister Adèle (or Alix) so that he could marry Berengaria of Navarra. Philip felt outraged and left Sicily before Richard's new wife arrived.
Second, they often conflicted during the siege of Acre. Philip was also probably a bit jealous as he was making strategies while Richard got all the credit because he was out on the field fighting.
2°) As was stated earlier in the thread, Philip got sick during the crusade. He lost nails, hairs and even one eye because of his illness. This probably played a part in his decision to go back to France.
Not to mention that Philip's succession back then was far from secure : he was the only son of Louis VII and had only one son, Louis, who was still a child back there (he was around 10). If Philip had died on the crusade, there would have been troubles.
3°) Several of the great French Barons who were with Philip died during the Third Crusade, most notably Philip of Alsace, count of Flanders, who died at Acre. Philip probably thought this would be of a huge political advantage to him : with so many great barons dead or absent from his Kingdom, he would face fewer opposition and be able to strengthen his authority (and he did). Plus, he had to play his part in the succession to Flanders and secure Artois for his son Louis (as Artois was the dowry of Philip's now dead first wife, Isabella of Hainaut).
Finally, this was an occasion to do nasty things in Richard's back, since he was no longer getting along with him and the Plantagenêt were a problem to Philip anyway (owning half of your kingdom generally gives you this kind of feeling

).
Without the Siege of Acre, Philip could stay longer on the Crusade, even if he and Richard are going to quarrel a lot. Saying that he will stay until the end is probably an overstatement though.