The Body in the combined photo is of a brand new unissued Lithgow made Body. The Steel Batch Marking at the front of the magazine well indicates the Body was made in 1970. Its not a reworked old Body, the reason its missing the L1A1 desination is Australiaproduced both L1A1 and L2A1 rifles and the Body is the same for both.
It was expected that the Base Workshop was to stamp/engrave the correct designation onto it, but this didn't happen. They were left blank. There are tons of examples in New Zealand of the bodies being replaced on the early L1A1 rifles due to 'stretching'. The cost of a new Body in 1981 was $132 AUD.
In the UKyou might of not replaced the Bodies, but in Australia and especially New Zealand we did.
Yes you're correct it would cause issues with illegal rifles being assembled, I've seen them as well as a L7A2. This is why in Australia there was a massive witch hunt at one of their supply bases over 'missing' 'unaccounted for' bodies, which in the end turned into a storm in a tea cup.