I've not found a solid reason yet, but I have several possiblities. First of which is Japan is known as the Land of the Rising sun, and the morning sun is red as it comes over the horizon. For the Japanese this powerful image may carry over into the rest of their day. So even though the sun is yellow later in the day, it's still thought of as being red.

Next red is a prevalent color in traditional Japanese culture, representing passion, energy, life force, vitality, power, and good fortune.

Red is also connected with protection, and expelling evil or illness. Some of the popular bosatsu, kami, and shitennô associated with red are: jizô, kannon bosatsu, daruma, fudô, inari, and zôchoten.

Finally red is warmth and life… literally; the red and infrared rays of the sun warm us and the earth.

Much of Japan is mountainous, has humid temperate weather, and is subject to both Pacific storms in the south and east, and subartic storms in the north. This combined with the lack of central heating in many of the homes and buildings, even today, frequently makes staying warm difficult. So it's the sun's warmth that is prized more than its light.

It's most likely there is no one reason, but a combination of all these. There are many connections betweens these ideas that work to make the red sun a Japanese cultural meme.