Interesting question. I've done a bit of searching around, and there's no obvious answer. Here's a theory: Think about what a plant does. It sits there fixed in the ground. It needs a ready supply of sunlight, water and nutrients from the soil - that's what comes in. Then there's a lot of processing going on : photosynthesis and stuff, converting light, water, chemical and organic compounds into vegetable matter. Sometimes even birds and insects get involved in the process. The whole organism works together and produces flowers, fruit, nuts, fibres or whatever else we need. It's a lot like nature's factory, isn't it? By the way, 'plant' has a subtly different meaning in US and GB English. In US English it's a countable noun referring to an industrial site, whereas in GB English it's an uncountable noun referring to industrial machinery. Hence the totally baffling UK roadsign warning 'Heavy Plant Crossing'. In spite of what you might think, this is not something from the horror movie 'Day of the Triffids'. It just means that that industrial machinery is sometimes brought from one side of the road to the other.

There is no answer to "why", it's just what the word means. Factory is another meaning for the word "plant". That's all- don't think too much!

Thank you. It is rare in Japanese. Instead, we have a lot of kanji.

Lots of English words have different meanings but the same spelling! :) Don't think about it too much.