Probably someone will build and sell a dirt cheap laptop with nothing on it except a basic word processor for this purpose.

It’s still a hard problem though. If the students have the laptops outside of the testing site, they can load cheating materials on them, or use them to smuggle questions and answers out if the test is used in multiple class sections. You realistically will not lock down a laptop students can take home sufficiently that some people won’t tamper with it.

Otherwise you have to have enough laptops to get each student a wiped and working machine for every test, even with lots of tests going on. And students need to be able to plug them in unless the batteries are rigorously tested and charged, but not every classroom has enough outlets. And you need to shuttle the laptops around campus.

Then you need a way to get the student work off the laptops. You probably want the student to bring the laptop up when done and plug in a USB printer. Anything else, like removable media, and you have to worry about data loss or corruption, including deliberate manipulation by students not doing well on the exam, and students claiming what got graded wasn’t what they meant to hand in. And you still have to worry about students finding a way to deliberately brick their laptops and the inevitable paper jams and other hardware failures, especially an issue when students need to leave on time to get to another class.

So you need systems that are cheap but reliable, tamper-resistant but easy to diagnose and maintain, robust against accidental data loss but easy to reliably erase, able to export data and install security updates without letting students surreptitiously input data, and heavily locked down while easy to use for students with a wide variety of backgrounds, training, and physical abilities.

Store in each classroom a custom-made rack for the laptops (with at least one laptop per seat plus backups). Distribute the laptops at the start of exams and collect them at the end.

The rack charges the laptops, streamlines distributing/collecting tests, prevents tampering, and reports defects. A professor uploads the test to their LMS and specifies the exam time-frame and location. Before the exam, the LMS transfers the test to the correct rack, which saves it to the laptops. After the exam, the rack loads the student responses and transfers them to the LMS for the correct class. Each laptop has a light under it whose color indicates whether it's in standby, waiting to be distributed (shortly before exam start), has a submitted test, or is malfunctioning (the rack periodically pings laptops in storage to verify they still work). Multiple professors can queue exams to the same location, in different time-frames, and the LMS and rack know when to prepare each test on the laptops.

The hard part is to implement this well. The rack's hardware and software must be reliable; nonetheless it will fail (hardware breaks), and exams get moved and rescheduled, so there must be a way to transfer tests to another classroom and time-slot. The laptops can have slightly less reliability, since there are backups; but failures can't be clustered, and if a laptop is transferred from another rack during an exam, it should download the destination rack's test and become active (so if one rack's backup laptops run out, laptops can be borrowed from other classrooms). The laptops must periodically backup in-progress tests using wifi or bluetooth, and if a laptop breaks during the exam, the student can resume their progress on another. Tests must be downloaded well before exam time, in case there are problems (laptops should be able to store and queue multiple tests). Laptops must handle exams that start late (up to the official exam end time) and end late (including overlapping the next exam's start time, in which case the next exam is loaded when the laptop is put back into the rack). The rack must absolutely not indicate that a laptop is ready with an exam if it's not; and (since tests are downloaded before exam time) nothing unique should happen at exam start time (to reduce last-minute surprises, and let a professor who isn't convinced take out a laptop and check that it's functional 15 minutes before). Last but certainly not least, the UI to submit tests and grade responses should be intuitive, simple (not overwhelming) yet powerful (can handle edge-cases like rescheduled tests, randomized tests, accommodations; or be extensible enough to support these features).

Despite all the above requirements I actually think such a product is feasible. Unfortunately, with firsthand experience of typical EdTech and academic bureaucracy (and I'm not a professor so I don't know the worst of it), I'm skeptical it would be adequate quality unless the company designing it is uniquely motivated and capable.