As is so often the case, a lot of my "why'd they do it THAT way?" questions on my Spridgets and MGBs were answered when I bought my '51 TD. The battery on that car wasmounted directly over the trans tunnel just in front of the firewall, same as on my first LBC, a 1974 Midget, or your Sprite.
It's a great place for central weight distribution, but viewed from a modern perspective, or even that of the MGB (with two 6V batteries behind the passenger's seats, right on the floorpan), it seemed to be a potential lever for weight transfer. My EP race MGB had a single 12V mounted on the right side of the trans tunnel, a demon tweak I later adopted on my daily-driver MGB. The main advantage: two fewer failure points if the battery connections got funky.
The Bugeye, of course, has access issues if you wanted to move it to the back of the car, as my Miatas, Lotus Cortina, and '91 E30 318is did, all the way to the back corner of the trunk opposite the driver. Great if you want to make an ad with the car balanced on a lever; not so good on a Bugeye, unless your pit crew includes a trunk monkey trained in R&R of the battery all the way at the back of the storage boot.
I did wonder aloud, once, whether there would be any advantage in mounting the battery on or just behind the (absent) passenger's seat of my friend's HP, and later vintage, Bugeye race car. His answer? He pointed to the exact spot I had identified, where the previous owner of his car had mounted an engraved brass plaque:
RACING IS A SPORT
WE DO IT FOR FUN
Fair enough.