I wouldn't say that there is anything wrong with running tracks under components.
Pad shape is vital for correct reflowing. For 0603 components and smaller the track underneath may restrict the pad shape, so that can lead to tombstoning.
My suggestion would be to get rid of all the neat lines of components if that can shorten the traces at all. You will almost certainly be sending the data to the pick and place machine electronically, so neat lines and only having components at 0, 90, 180 and 270 degrees doesn't actually make life easier for anyone.
It can also help the soldering to keep the number of connections per pad down to 1 if possible, by joining tracks away from the pad.