No it is not necessary, and the research supports the fact it is not necessary. Whatever the stimulus is, there is a response.
In practice, it depends on if your goal is to get a swoll look (hypertrophy) or to increase strength. For increasing strength I personally don't recommend training to failure because you're more likely to get more stimulus in by doing multiple low rep sets at the high weight than by burning them out in the first set and having to reduce the weight, thereby reducing the amount of volume at that high rep.
Also, I don't understand why you would do an ascending set unless you are trying to figure out how much weight you can lift safely or if your goal is purely to burn your muscle out. You know your strength better with descending sets after you know what to start with by doing an ascending set for a few weeks.