The question asks for the "necessity"/"why is necessary" to do the checksum test. Even though or maybe because of I assume a security context I am a little troubled. I assume you meant to say somehting like "what would be the security gain of using same origin plaintext transmitted hash/checksums"?
No, it is not very much useful to the safety/security
As you might have stated already with your sceptic/bright question the security gain would be in many cases quite limited. If somebody is able to tamper a 600MB download on the fly as a "transparent Man in the middle" that attacker is surely able to generate a fitting hashfile that will prevent you from noticing the tampering of the 600MB file.
The (not so much security related) reason - data curruption at transmission the data has been stated also already.
I do not want to provoke that new additional point here as "a very secure feature" but if you perceive an attack under the light of its effort and costs. It might be that an attacker is well able to tamper a 600MB file (which takes some time do download) at one or two points of time. The hash/checksum file (which as @Thomas Pomin put is quite so well concentrates the security requirements) can be downloaded more swiftly (only few bytes). It can be easily be downloaded several times (at different point of times). Without any big effort from your side (since the file is so small) but would require the attacker to be constantly on the watch somehow. The fact that the hash concentrates the security makes might make shift the "effort ballance" to your side. You would not download the whole (let's say 600MB*.iso) for 3-4 times just to check if it is still the same (i.e. that there is no obvious sign of tampering the data), but you might consider downloading (at very little expense, the hash from multiple source at different dates). The effort (thanks to the hash is little) for your. No matter the attacker has to be there (even for the few bytes, otherwise the not fitting hash/checksum can indicate some discrepancy).
Of course you can consider that this is only a very thin, small added security (resulting from an potential increase in the effort it takes to successfully run the attack) but since the hash can be computed and transmitted (several times, multiple sources) it can promote an increase security.
regarding multiple source:
Your examples given can be seen as
combo. allowing you to download the iso via HTTP (saving the computation power of encryting the transmission) and then downloading the HASH/Checksum via HTTPS in order to reduce to some extend the chance of an attack.
Just to mention it also. There are often also file signatures used which do not only contain a hash value but are by using public/private key signing can be checked for authetity or origin and will beat (in terms of security) the only hash-value/checksum files.