The testing situation you describe sounds like a multifactor problem with multiple possible solutions. It could be that a concern for cheating is the key concern here, but logically speaking, there are several distinct factors that could play a role. Someone can be concerned about cheating and still create a fair test. From an instructional design perspective, I'll name the most important factors I see and then list a few possible solutions.
Raw Difficulty / Learning Objectives
A math test can be easier or harder depending on what the instructor asks students to do, how much work they should show, and so on. For instance, compare solving an equation for x or finding the derivative of f(x) to interpreting a word problem, or solving a fairly simple equation with a more complex one. Compare working with separate questions with sequential questions that build off of the previous question's answer. The selection of these problems is often guided by an instructor's implicit or explicit learning objectives for a unit.
Time to Complete Test
In test design, instructors need to be very careful that students have enough time to give a fair attempt to each problem. Instructors can develop different rules of thumb. Some base completion time on how long it takes them to complete the test multiplied by a factor of two, three, or four. Others estimate the time for completing each problem and sum up a goal time, which might come out to 40 or 45 minutes.
As you point out, many instructors don't account for how test format determines timing. In a paper test, a viable test strategy is to read the entire test and focus on easy problems first. In contrast, the testing systems in many Learning Management Systems either make scrolling through the test difficult or restrict movement between problems. So if a student is stuck on problem 3 of 9 and spends 15+ minutes on that one, they have no way of knowing when it's better to cut and run to an easier problem for them. Thus a test that might take 40 minutes for a student on paper would actually take closer to an hour.
Concern for Cheating
So the concern for cheating is a factor that affects how the instructor has implemented these other factors. You describe the time limit and test format as factors affected by a concern for cheating. In particular, students may have less time to share answers or look up information. Yet there are also other anti-cheating formats used. For instance, some professors have proctored exams, even online, which involve some kind of visual monitoring.
There are more factors, but what's to be done? You can toggle any one of these factors in order to increase the pass rate:
Have fewer problems, or easier ones. In other words, adjust the total difficulty of the test so that students can complete it in the allotted time.
Make the test time longer. Giving an hour rather than 50 minutes, for example, may have enabled more students to complete problems.
Allow students to see the whole test when they start. That will let students prioritize the problems they know how to solve, rather than being at the whim of the instructor's own design or an RNG algorithm (if order is randomized).
Worry less about cheating. This may mean adjusting any of the factors above, or it may mean rethinking the format itself. Think critically about whether your summative assessment needs to be a test, or whether it could be a project, homework, or something else.
Finally, any instructor who has been in the classroom for some time knows that they assign unbalanced assessments sometimes. It happens. If the end result is an average of 50%, an instructor has other options to mitigate the effects of unbalanced assessment on student outcomes, like grade curves. So whether or not the concern about cheating - or some other factor - produced a test that was difficult for students to complete, instructors have several tools for adjusting future tests and even addressing this current situation.