Total Time Accounting is something typically seen in projects contracted by Government entities, based on a few quick Google searches, and this article:
Government Contracting Leader - UNCOMPENSATED OVERTIME AND TOTAL TIME ACCOUNTING
In government, as well as many rigid corporations, process is king, and there are huge departments of people whose job it is to audit these reports.
In smaller businesses that aren't so regulated, this type of time tracking just isn't necessary, and it may have more costs associated with maintaining it than without. These costs could be monetary, but these costs could also be mental. Any time spent documenting time for each and every task takes energy away from actual work and thought on those tasks.
Accordingly, all government contractors should ensure that their time charging system is capturing all hours worked and allocating the cost to all hours worked using one of the aforementioned methods. Doing so not only requires investment in compliant accounting and timekeeping systems, it is also requires the implementation of effective policies, procedures and employee training programs.
While the author uses the term "investing" when talking about accounting and timekeeping systems, senior management will easily see this marketing-speak for what it really is, additional costs. Policies, procedures, and training programs also imply additional, unnecessary expenses in the eyes of senior managers.
Additionally, many smaller businesses just don't require this level of accounting. Also, senior managers would prefer to look at the strategic big picture rather than the details. As long as a profit is generated, that's all that matters to them.
Finally, engineering isn't the same field as one that involves preparing your burger and fries. Engineering is fundamentally not an hourly position. It involves creativity, ingenuity, intelligence, autonomy, and decision making abilities. Some of the best ideas even come when engineers are stuck in traffic, in the shower, sleeping, or awake at 3am. The question is how to objectively measure such subjective gains in a project.
Senior managers may view this level of accounting as not making sense, but also they may see it as not having measurable value and being riddled with more productivity-robbing costs.