Perhaps it's not the lax use by Jedi that is at fault. I'd assume that a Jedi would be quite comfortable using their weapon with little effort, so to give that rarely used feel to them seems ... off.
To me, the problem lies in the lack of public respect of Jedi as a whole that is shown in the PT. Rarely are their actions truly praised, and you never really see Jedi in action just generally doing good deeds. Jedi should be shown rescuing children from wreckage, where the children look up at them in awe and wonder, completely thankful and knowing they are safe because of the Jedi's presence.
We never feel that presence, because the people they generally interact with and protect are either high ranking so there is less sympathy, or just generally unlikeable. The only reason that Yoda and Mace Windu (and Ki-Adi-Mundi) maintained that feel of respect is because they were obviously looked up to within the council. And you can think it's stupid or hate it all you want, but I have more respect for a lightsaber when Yoda first pulls his out of his cloak in AotC (ignore the jumps and flips and just focus on the drawing the lightsaber), than any time you see Anakin flippantly pull his out.
To me, lightsaber equals jedi - If the Jedi isn't revered, there will be little to no reverence for their use of a lightsaber.
It all comes down to putting characters into situations that the audience can connect with, without overdoing it and shoving it down our throats...
Because I can imagine Imperial Troops holding a group of women and children hostage with an Army of Stormtroopers marching through the mist, and 10 or 15 or even more Jedi attacking this huge army, trying to break through to save the innocent and helpless. Storm trooper heads rolling, blue and green sabers slicing bodies to the ground, blasters taking out Jedi. Utter chaos, watching the kids look on in fear, their mothers crying, trying to soothe them and stroke their hair...