There is a natural healing mechanism for lost branches, sealing off a branch doesn't affect the main transport system of the tree.
Trees don't "heal". Animals heal.....Animals (including us humans) are able to regenerate, as cells die so new ones are made to take their place. Trees are generators, they cannot regenerate but only generate so they have developed a system we now call "CODIT", which stands for Compartmentalization Of Decay In Trees. This term was coined by the late Dr Alex Shigo, an eminent tree pathologist, who is widely accepted as the father of modern arborculture.
Basically, the tree changes the chemical formation of cells around the wound to create a barrier zone to slow down the rate of decay and/or infection, if I remember correctly it cannot stop it but can slow it right down, even containing it to the end of the trees life (which could be considerably shorter than its natural life if it gets felled of course), hence wounds that look like they have been contained in felled timber would in fact be still active albeit slowed right down by the trees barrier system. When a tree is felled and therefore dead, the rate of decay would increase.
In a living tree as it starts to create its barriers around the wound the tree also starts to "generate" more cells and grows new bark and wood cells around the outside of the wound to seal it from anymore environmental factors, fungi, insect pest, water ingress etc so we see what looks like the tree "healing", it isn't....it's "Sealing" and compartmentalising the wound.
Each and every time a tree is damaged the wound stays it doesn't heal, it can't heal. Now, trees have got pretty good at CODIT and can survive many wounds but just as with most things, if you get wounded enough or in a big enough way....you will die and so will trees.
The other factor to bear in mind is that trees store their energy in their living cells, each time a tree is wounded and has to adopt its CODIT defence it is losing storage space. It cannot store energy in the dead decaying cells or the chemically changed barrier cells so it has less cells to use for storage. If it sustains too many wounds and therefore does not have enough energy stored up in itself then it would be particularly susceptible to external environmental attack in whatever form.
So don't feel too bad for wounding trees that will never heal, we've all done it and some of us do it for a living but lets try and do it as best as we can for the tree.
I very much recommend the works of Dr Shigo to anybody that has an interest in trees, it's really very interesting stuff and I find his writing so easy to follow.
Hope the above makes sence.....clearly I'm not tree pathologist lol