Yes, it definitely will not work to plug covert channels or side-channel attacks like Spectre. Typically, computers without MMUs also don't have speculative execution, or in most cases even caches, so Spectre specifically wouldn't be relevant, but lots of other timing side channels would. Maybe other side channels like EMI and power consumption as well.

But consider, for example, decoding JPEG, or maybe some future successor to JPEG, JEEG, by the Joint Evil Experts Group. You want to look at a ransom note that someone in the JEEG has sent you in JEEG format so that you know how much Bitcoin to send them. You have a JEEG decoder, but it was written by Evil Experts, so it might have vulnerabilities, as JPEG implementations have in the past, and maybe the ransom note JEEG is designed to overflow a buffer in it and install a rootkit. Maybe the decoder itself is full of malicious code just waiting for the signal to strike!

If you can run the JEEG decoder in a container that keeps it from accessing the network, writing to the filesystem, launching processes, executing forever, allocating all your RAM, etc., only being permitted to output an uncompressed image, even if you let it read the clock, it probably doesn't matter if it launches some kind of side-channel attack against your Bitcoin wallet and your Bitchat client, because all it can do is put the information it stole into the image you are going to look at and then discard.

You can contrive situations where it can still trick you into leaking bits it stole back to the JEEG (maybe the least significant bits of the ransom amount) but it's an enormous improvement over the usual situation.

Then, FalseType fonts...

Well, they may not have speculative execution,but some of them do have branch prediction these days; which probably leaks a certain amount of information. Eg, the cortex M7 (no mmu,mpu optional, has branch prediction)