I think there are a few main kinds of reasoning behind DRM (non-exclusive, more then one could be involved in any specific case). One is psychological, one is pure greed and generally not explicitly acknowledged, but the last is potentially reasonable in specific situations.
The first essentially boils down to the well studied psychological phenomena of Loss Aversion, which is what you refer to and purely emotional, the feeling of "someone is TAKING my work!" It has been very well studied that humans in general have a strong natural tendency to prefer to avoid losses vs thinking about gains, and in fact the psychological power of losses can be vastly more (2x+) vs gains. This phenomena is used extensively in marketing and other areas involving behavioral economics. It is not usually logical, and particularly not in the case of IP infringement where the emotional response fails to consider both that there is no actual loss and that IP itself is not a natural construct and imposes societal costs. Nevertheless, it's definitely powerful and it fuels some of the emotional outrage many honestly feel at infringement, even if it's not merely illogical but outright economically self-destructive (they spend more on DRM and cause more pain to legitimate customers and in turn drive them away then they ever get back).
A second, purely greed one, comes down to controlling power. A lot of big publishers/organizations in particular saw (and still see) DRM as a way to extract far more money and rent seeking through extreme personalized spatial and temporal slicing of IP licenses. Basically, a much more extreme version of what the music and movie industries saw with the various format transitions (tape to CD to online, VHS/DVD/Blu-ray/online). Those were enormously lucrative since they could simply take existing IP and repackage it and sell it all over again, repeatedly. Their golden vision for DRM was payments not just for formats but everything. A different fee to play in each car, in each player, per units of time, every new bit of hardware, etc. Fundamentally DRM represents arbitrary control beyond the bounds of law, and that control can be used for a lot more then merely preventing infringement. Fortunately this vision was at least partially thwarted, but it'll be an eternal battle as lots of money will always be on the table here.
The third most arguably legitimate use is an extremely time-limited-then-eliminated application for the kinds of major entertainment IPs that experience extreme reverse J-curve demand patterns. Ie., a majority of total lifetime demand may come in the first few days/weeks/months before exponential falloff and a move into low long tail territory. This can simultaneously represent the time when costs are highest too, due to factors like simultaneous online resource demands and (in the case of video games) ongoing development work/support engagement. For movies and video games your numbers (10 vs 1000) are backwards or worse, an enormous number of people will pirate if it's convenient enough. But these are very low effort, casual pirates, not dedicated ones, and they also are time pressured. They aren't fundamentally unwilling to pay for whatever it is either if they have to because they want it right then to be part of the cultural zeitgeist and experience the social networking at its peak period.
In this last situation, limited time DRM can be a practical choice in some cases. If it's cheap enough it only needs to last a month or two, or even just a few weeks, to generate significant economic return. Then it can be completely removed for the long tail as the entertainment IP gets into sale territory, which may bring in some more people who care and eliminate ongoing support costs as well as ensuring that all existing owners will not experience problems as the publisher attention winds down.
Of course, getting rid of it there promptly is key and something that publishers too often ignore (or they're actually looking towards #2, and hoping to monetize it in other ways with the aid of ongoing control). In principle though this is relatively innocuous, since the biggest practical problem with DRM is in the longer term. If for example it was mandated by law that all DRM had to be removed within 6-12 months of an IP launch it wouldn't be ideal and there'd still be moral concerns and arguments but it might be a practical compromise too given the realities of human psychology.