Aren't most of the calorie-dense foods vegetarian? Peanut butter, for example, contains 1600 calories per cup. A meal of pasta with an olive oil-based sauce will easily get you over 1000.
Yes, a lot of completely vegan foods tend to be very calorie-dense. There are quite a number of non-animal sources of
bio-available protein that are higher density than meat (which has a fairly poor ratio). The only trick to vegan protein is getting the right balance of amino acids; and that's hardly rocket science. Meat is historically preferred among hunger-gatherer and early-agrarian cultures because it's fairly dense, and has a well-balanced amino acid profile. Most vegetable protein sources that carry the highest number of necessary amino acids are lacking in one particular one, lysine. Animals that eat those sources exclusively manufacture their own lysine. Humans do not. However, most grains, while being low in other amino acids, are very high in lysine; which allows a very simple diet to provide all necessary amino acids in sufficient quantity.
And you hardly have to eat massive quantities, since good sources of both are higher in bio-available densities than animal sources. Add to that the fact that most people, at least Americans, typically get several times the amount of protein that they actually need in their daily intake; that "problem" is pretty effectively debunked.
HDL fatty acids are very easy to get from vegan sources; which are much healthier than meat, since most animal sources have a poor HDL/LDL balance. Interesting note, there are several vegan fatty acid sources that have HDL/LDL balances worse than any animal source - namely Coconut oil and Palm oil. They're very commonly used in junk food.
There is only one nutritional problem with a purely vegan diet; and that's vitamin B12. This can be tricky, as there are very few vegan sources; and most of those have low bio-availability (due to absorption-blocking analogues). The one exception being certain strains of nutritional yeast; which contain high levels of B12, with a high bio-availability. However, it's still not a serious issue, since physical requirements are very low and B12 is recycled by the body. It can take 10-20 years under normal conditions before a lack of B12 begins to cause adverse effects. Supplements will eliminate any problems; and a lot of pre-packaged vegan foods are supplemented with B12. Again, hardly rocket science. In fact, severe cases of B12 deficiency are more common in non-vegetarians; typically those with poor diets, and heavy use of other substances which deplete or block absorption of B12, such as alcohol or tobacco.