I do keep the flowers on pulmonarias as long as I can as they are much visited by bees and orange tip butterflies - can you spot one here?
But they are very prone to mildew and can look awful after flowering with the whole plant sometimes dying back.
I find that cutting back all the flowering stems (which get the mildew) encourages the plant to throw up new beautiful leaves.
And quickly! This was taken on 24th June,
and this on the 29th.
A lot of growth in five days, and it will continue growing new leaves and looking good all summer.
If you don't have the time or the inclination to cut every individual stem you can just take the shears to the whole plant - it will recover, especially if you give it a good soak afterwards.