I just wanted to relate my personal experience here in case anyone else ran across this question in a Google search.
I can't answer the question why from a strictly electrical engineering perspective, but I can answer the question from a practical real-world use perspective:
I have an entry-level Klein-branded multimeter and it was time to replace the original generic 9-volt battery which it came with out of the package. I thought I might try one of those Energizer Ultimate Lithium 9-volt batteries (the very ones you pictured in your original post).
It just wouldn't work. The batteries were brought brand new (new stock) and I used one directly from the package. The multimeter would turn on, but it would sometimes flash random numbers. Sometimes it would turn off. Sometimes it wouldn't turn on. If I tried to test a circuit sometimes it would give me a voltage reading, sometimes it wouldn't. If it gave me a voltage reading, sometimes it looked correct (I was working with a "known" quantity of ~120V AC) and sometimes it looked untrustworthy (like 96V). Sometimes it looked like it was counting up to 120V but then would freeze at 96V or something. Speaking of freezing, if I got a voltage reading it would always freeze after the first reading. It wouldn't update the screen, even if I removed the probes from contact. I always had to restart the device just to hope to get a reading.
Bottomline: it was random and unreliable and basically useless. If I'm trying to test for a live wire and I don't know if the 0V I'm being shown is because the screen is frozen or not, it's a useless device. If I'm shown a reading but have no idea if it is a real, valid reading or not, it's useless.
Later I purchased a normal Rayovac 9-volt battery and the multimeter went back to working just fine.
So, from a real-world practical perspective, you can't use a Lithium 9-volt battery in at least some multimeters because they just won't work correctly, or reliably, or at all.
From an electrical engineering perspective, I assume some multimeters just weren't designed to handle the slightly different voltage output of a Lithium 9-volt battery. The internal circuitry is just too sensitive to voltage outside the design spec, which expects the voltage output and curve of a standard 9-volt alkaline battery.