Loose bass, forward midrange, bright glassy upper mids/lower highs, rolled off upper highs. Variable performance. Unreliable. High maintance. Difficult to get replacement parts. When they break, they offer the potential to break other links in the system. Excessive heat. Potential burns to children, pets and others. Can cause fires. Requires more care in placement. Limited to use with high impedance speakers. High cost per Watt. Greater sensitivity to speaker cables. Sensitive to vibrations.
Why all the fuss - most of this is quite true although it is a matter of degree. Perhaps Unsound paints an overly negative description for sure, but if you asked people to make a general list of all the cons against tubes they would probably come up with at least four or five items from Unsound's even longer list.
Of course there are a great many pros for tubes starting with their sweet organic, harmonically rich, engaging and musical sound but the OP didn't ask for that.