Since Cailan did write to Queen Celene for aid I think he did see the darkspawn invasion as a serious threat. But after the third battle he began to doubt it was a true Blight and just became cocky with all the victories. Of course, he was being foolhardy being on the battlefield at Ostagar. He should have commanded from further away. Nobody had seen the archdemon, which means they never thought the darkspawn were being directed by a smarter mind. Youthful enthusiasm with naivite, but he truly believed in uniting all the people to fight the Blight.
"Commanding from far away" was effectively impossible in mid-battle before the advent of, say, firearms (when formations generally stopped getting tangled up in each other so much as soon as a battle started). It'd have been utterly pointless; the king might have been able to see the whole battlefield (emphasis on might) but certainly would not have been able to send orders and direct troops that were already engaged without opening up a horrendous amount of delay. When an hour could pass between the issuing of an order and its execution, the tactical situation had almost always completely changed anyway, making the order useless at best and actively detrimental at worst.
We do not speak of Schlieffen's "modern Alexander" with telegraphs, telephones, radio, cars, and planes to speed messages along; we don't even speak of a
Medieval Total War commander with instant, perfect reactivity to orders issued and instant, perfect information on which to base those orders. We must, as Loghain said, attend to reality, and reality is that a general who stayed away from the fight would be as useless
during the fight as though he were on the far side of the Moon.
In concrete terms, the king's personal presence with his men added little than the skills of a single soldier, true enough. And a king's death in battle - especially given the lack of an obvious successor - could be catastrophic for a kingdom, as it was for Ferelden. But the king was not merely a lawgiver and ruler and symbol. His political power descended, first and foremost, from his role as military commander: defender of the realm and his subjects, destroyer of their enemies. Medieval European rulership was highly ritualized around kings' martial roles. And failure to perform the ritual properly - whether that meant a procession into a city or participation in battle - eroded anybody's interest in having that particular king around.
Put another way, not participating in battle meant that a king could very well be accused of not doing his job. And
participating in battle accumulated glory and prestige almost regardless of battle's outcome. Contrary to Loghain's complaints, military glory was very much a currency one could spend as a ruler. It had meaningful value: in diplomacy, in internal politics, and even in operational maneuvering. A blooded warrior-commander commands significantly more respect from both subjects and military opponents than does a callow tyro general.
Cailan comes in for censure in this thread not because of
process. A long line of historical warrior-kings, and the laurels they gathered in battle, attests to that. He comes in for censure because of
result: his army lost at Ostagar, whether because of him or someone else, and he died in battle, and his death sparked a civil war that nearly destroyed Ferelden. But that result was based on a coin-flip, as battle always is. Set-piece engagements are lotteries, as the truism (correctly) goes. And it was a necessary coin-flip, because there is no other way to defeat darkspawn than by killing them: operational maneuver is pointless because of the non-combat effect of the Blight.
Cailan was unlucky, and he was a victim of a traitorous subordinate; he did not exhibit particular military skill but it's unclear that any such skill would have been enough to save either himself or his army in the face of Loghain's betrayal. And it's further unclear that any better plan existed than the one that led to the final catastrophe at Ostagar. If that counts as digging one's own grave, well, the answer to the OP's question is 'yes'.