Your advantages with the 70-200 f4L are 1. The price is very reasonable for L quality
2. The lens resolves a lot of detail ! It is optically as good as its bigger brother, the F2.8 is. Albeit yu do not have the advantage of the extra stop.
The physical size and wieght make it a good walk around lens compared to others in its focal length range.
It is white and therefore has a cool factor and occasionally people will see you carrying it and automatically assume you are a professional. Those who know about photography may be impressed with your quality toys!
Unfortunately there are downsides to consider.
1. It can be a hit and miss situation trying to get one that does not have some focusing difficulties. Bummer huh? I have owned mine for near two months and have had nearly no chance to use it effectively because after recieving ot, I had to return it for an exchange for the focus problem. After I recieved the replacement, it had the same problem. I opted to send it to Canon USA for service along with the camera. 10 days later I got the camera back but the lens needs a part they say. They have not got the part so I am waiting for them to get it and hoping after they get it and instaqll it and send me the lens that it will function as others like it do. As I said, this lens is known to be really sharp.
2.The F4 limits you to a large degree as far as low light photography is concerned. It is a great outdoor performer even for some sports. No good for indoor sports with much action. TheF4 aperture means you will lose the ability to have auto focus once you add a TC.
Since you mentioned the desire to add a TC in order to get upto 400 mm, you may want to give more serious consideration to a Sigma 70-200 F2.8 lens. That one is said to be almost as sharp as the Canon 70-200 F4 at F4 and up. It wouls allow you to use a TC and still have the auto focus. It is black so you would have to do without the prestige but maybe gain some ability to better do candids. The Sigma is heavier although I do not know how much so. That lens is only a little more expensive than the Canon. Someone else mentioned the Bigma. Yea, that is my next lens I am almost certain. It is big, it is heavy, it is black but that baby has some reach and as long as you have some light to feed it, that lens can produce some real sharp images. Choices, I wish you the best in deciding. I wish me luck in regards to mine coming back from Canon being the performer others have in the 70-200 F4. If mine is not on the money when it comes back from Canon, I will be getting rid of it.