Alistair and the warden were perfectly aware that Duncan was killed by the darkspawn and that they lighted the beacon too late since they both were assigned to the task.I may as well say that Alistair was responsible because he missed the timing of the signal and not Loghain.
Loghain's death at the landsmeet serve nothing other than satisfy revenge and placate Alistair while his joining is actually more fruitful than his death which is objectively useful only vs the Archdemon.In Ostagar Loghain saved a large part of the army so what he did was reasonable as well as intelligent and it wasn't desertion he changed the plan when it was disrupted by those two warden who lighted the beacon too late.
There are plenty of accusations that can be made to defeat Loghain but Ostagar is not one of those.
I think DAO fans will be debating this issue till the next Blight! If the PC and Alistair lit the beacon too late, it was because Loghain's soldiers had lost control of the Tower in the first place!
Going back to the original battle plan, Cailan's forces were supposed to engage the Darkspawn hoard while Loghain's forces were kept a safe distance away, out of sight of the Darkspawn Army. (Would the Darkspawn have charged Cailan if they saw that Loghain had an army in position to flank them or hit them from the rear?) At a crucial moment, Duncan was to signal the Tower, and the Tower guards (plus the PC and Alistair) were to then light a signal from the Tower of Ishal that would be visible to Loghain. If Loghain is close enough to the battle to see how badly Cailan's forces are doing, shouldn't he be able to see Duncan's signal as well? And if Loghain is that close, why bother with the Tower signal at all? I believe the cut scene they show after you light the Tower signal is misleading. If Loghain is so close to the battle that he could clearly see what's going on, he should be able to know when to attack without the tower.
All that said, Alistair's hissy fit over recruiting Loghain is annoying. But keep in mind, he really doesn't know that much more about the Wardens than your PC. When you meet him, he thinks it's odd that Duncan would recruit a cutpurse like Daveth as well as a respected knight like Ser Jory. He also doesn't know about the US. If he did, he might appreciate that recruiting Loghain might actually give him the vengeance he wants.