Actually, I agree with you! But if this is so, why are many double bassists so interested in using directional mics for their close placement with H-Clamp, various contraptions or just a piece of foam to hold it in place next to the bass? Many times it seems like using omni isn't a consideration.
The correct answer varies with the situation and your goals. Sometimes an omni is better and sometimes a directional mic is better. I believe the only place I have ever used omnis in a live setting is drum overheads, and the drummer was on the back of fairly deep stages.
If you are playing solo, the omni will most likely sound better closer to the instrument. The directional mic may focus in too narrowly on the instrument so you really don't get a true representation of the composite sound produced by the total instrument. Also the directional mic rejects more of the room, which might actually be pleasing.
If the omni is too far from the instrument, it will most likely pick up too much of the room and not enough of the instrument.
If you are playing with an ensemble you may be willing to accept some of these trade offs in order to benefit from the superior off axis-rejection of the directional mic. Basically you use the directional mic closer than it's optimal distance in order to focus on your primary sound source and maximize rejection of bleed from other instruments.
You should also consider the inverse square law: For every doubling of the distance from the sound source in a free field situation, the sound intensity will diminish by 6 decibels. This has some relevance because you may be able to place the omni mic closer to the instrument and still get a decent sound.
I am used to performing in mostly loud settings with a fairly powerful amp. I would be very surprised to find any mic or mic techique that would meet my expectations in a big band setting, and yes I have experimented with some nice mics. But plenty people seem to think mics work fine on bass in big band. They have a different philosophy, use a different approach, and have different goals.