Where are you getting that from? I've never seen anything that suggested that the peace proposal was anything less than a good faith effort to resolve the Succession Wars.
Yes, but it's worth asking 'on whose terms?'
What does 'resolve the Succession Wars' mean? Katrina's peace proposal didn't resolve the question of who would be First Lord, for instance, and that's ostensibly what the wars were about. The peace proposal was a serious proposal to
stop fighting, but - who would want that, why, and what long-term issues does it resolve?
The Lyran Commonwealth is the economically and industrially strongest of the great houses. By its very nature, then, it has the most to gain from a cease-fire. It benefits the most from a pause to rearm and rebuild. If I were Takashi Kurita, why would I even consider consenting to that? All of my interests seem to favour keeping the pressure on the Lyrans.
Looking at it with the benefit of hindsight, I think there's probably a fair case to be made that Houses Davion and perhaps Liao were the only ones likely to benefit from the peace proposal. House Kurita loses from that proposal: given time the Lyrans will out-build them and out-tech them, whereas raiding and attritional warfare are the best way for House Kurita to counter that strength. The Mariks are in the same position, even if it's not quite as extreme for them. Look at the twenty years or so immediately prior to the peace proposal: the Mariks hit Coventry, Alarion, Bolan, and Pollux in 3006, and in both 3015 and 3019 sent Wolf's Dragoons on a series of industrial raids, the latter a serious attack on Hesperus II. Both the Kuritas and Mariks were engaged in pretty aggressive raiding to try to blunt the Commonwealth's industrial edge.
In the 3010s, Katrina's overall policies seem pretty defensive: she pulls Lyran forces back, strengthens garrisons, reassigns dropships to humanitarian aid and industrial development, and so on. She's trying to back off and build up. In that context, she then proposes a general cease-fire. I can completely understand why House Steiner's two closest enemies reject that. It is obviously a move that disproportionately benefits House Steiner: "please stop hitting me while I try to rebuild."
It's Houses Davion and Liao who have the most to gain from peace, since neither of them have any particular reason to fight the Commonwealth. Indeed, both would probably benefit from a stronger Commonwealth taking the pressure off the Kurita and Marik fronts respectively. It's not that the Liaos or Davions are nicer or more peace-loving - it's that peace and Steiner build-up supports their interests. So Katrina looks more closely at both of those, and comes to the reasonable conclusion that House Davion is more trustworthy, has more shared culture with the Commonwealth, and has more to offer in an alliance.
As far as I can tell, IU voices generally agree that the peace proposal, while in one sense sincere, was also clearly something that disproportionately benefitted the Lyrans.
3020 was also the year that Archon Katrina Steiner issued her 'Peace Proposal' to the other Successor States. Even though her proposals were nothing more than a glorified attempt at a cease-fire on her terms, the eagerness with which Hanse Davion entered into a dialogue with Katrina Steiner surprised even the members of the esteemed First Circuit.
In 3020, Archon Katrina Steiner went one step further by issuing the Peace Proposal of 3020. In it, she wrote that the hope for reuniting the Star League through force was a very dim one that could only lead to more bloodshed, that every Successor State should be content with what it had and cease the wasteful warring over worlds. She suggested that the five House leaders arrange a cease-fire to last for several months, so that they could meet on Terra. Once there, the five might be able to work out individual treaties, with the exalted First Circuit of the ComStar [sic] acting as a neutral witness. The Archon's proposal then outlined a system that would channel their competitive urges into economic adventures so that disputes over worlds would be won by whomever could best economically develop the planet.
The other four Successor States rejected this cease-fire initiative. Aside from the Draconis Combine, which did not deign to answer, the other three replied that this proposal for an economic free-for-all would play into the Commonwealth's hands. Everyone knew, they said, that the Commonwealth had the best industrial base from which to wage this economic war.
I would note also that the stated justification for the peace proposal given here is ideologically impossible for both the Combine and the Confederation. "Let's all stop and be happy with what we've got" is not a proposal that House Kurita can agree to, as they're committed to the view that they ought to control everything, or that House Liao can, as they're committed to the idea that they must 'liberate' every single ex-Capellan world.
And the economic competition bit is just... yeah...
How would the other houses respond if House Kurita proposed that we abolish war and resolve all territorial disputes by ritual
iaijutsu duels? ;)
I think Katrina sincerely wanted peace, and sincerely would have really wanted the proposal to go through, but she was smart enough that I don't think she ever seriously believed the proposal would be accepted. The point was to buy time, and perhaps to send out feelers and discover which of the other states might make good allies.