Yes, tree topping is bad. When you top a tree, you create more work down the road for yourself. Suckers that grow back grow out of the cambium layer just under the bark are very weakly attached. As they get bigger it is common to see them break off. Topping a tree also make it look ugly, and this damage is irreversible. Once a hatrack, always a hatrack.
Reducing cuts are preferable to topping cuts. Reducing cuts take the limb back to a junction or crotch. These cuts reduce the length and weight of branches as well as leave the tree looking natural, as if it just grew that way.
That said, there are a couple trees that like to be topped, and even should be–it isn’t the Siberian Elm though! Any fruit tree where we really love the fruit should be topped nearly every year. Fruit trees can tolerate mostly every branch being cut off, and they still thrive. This process keeps the fruit where we can still reach it, and prevents the tree from getting overgrown. Willow trees also like to be topped, and can also tolerate nearly every branch being removed. This is partly because willows will naturally shed their branches, which many willow tree owners are well aware of—they are quite messy. When topped correctly over the years, a burl may develop on the trunk where new branches will readily grow.
Elm trees should not be topped, but rather thinned, reduced, and pruned away from buildings. Although they will survive, suckers that grow back will be weakly attached, and the tree will be ugly. This tree will need maintenance for the rest of its life, and there is no way to make it look like a tree again. Consider removing these trees instead.
Many other trees, like oak, or locust, will usually just die from the stress of topping.
This is a tricky question, because it depends on why you want to prune the tree! Most trees can be pruned at any time of the year, especially if the goal is to remove the dead, dying, and diseased branches; thin and shape the tree; or trim the tree away from a building or electric wires. Personally, I like ornamental pruning in the dormant season (winter), because the branching structure is more easily visible since the leaves are gone. I can still tell which branches are alive by the presence of buds.
Fruit trees, when used for agriculture, are best when pruned just after fruit drop. This gives the tree more time to grow after pruning, and just before going dormant, the tree will make the flower buds for the next year. If you prune after the tree is dormant, you will cut off many flower buds that the tree has already created. If you remove all the flower buds, it follows that you will have no fruit the next year, although the tree is likely to live. If you remove some of the flower buds, anytime before fruiting, you will get larger fruit. More flowers is to plentiful small fruit, as less flowers is to less plentiful larger fruit. Knowing this, if the tree’s purpose is not the fruit, but rather the flowers, then we want to prune just after flowering.
Be careful not to prune too heavily before the hottest part of the year, as stress and sun tend not to mix well.
As with most tree troubles, there is no way to diagnose without first identifying the species, taking a first hand look at the site and obtaining a full history, however I am highly suspicious that your tree may be infested with the Douglas-fir Tussock Moth. The Douglas-fir Tussock Moth affects Douglas-fir, white fir, and blue spruce in Northern New Mexico, and can easily remove all foliage in a few years, usually starting at the top. The overwintered eggs hatch from mid May to early June and the baby caterpillars feed on the new growth. They are compelled to climb as high as they can to release a silk parachute to carry them away in a breeze in hopes of finding a new host tree, but most perish on the journey. This compulsion of the young to climb upward may be what causes just the top of the tree to die, but it is actually the mature Tussock Moth that does the most damage which can kill the rest of the tree.