In my experience SM58s are particularly bad about picking up bleed from the snare and cymbals. Part of the issue is the SM58 is very forgiving about mic technique, which can result in the vocalist singing too far from the mic. For maximum bleed rejection, the lips should be touching or close to touching the head of the mic, especially with a weak singer.
A more directional mic can definitely help. But as others have said, it won't totally fix the problem alone. Also, more directional mics are less forgiving about mic technique, so the vocalist must sing right on top of the capsule. If they sing too far from the mic, it won't pick up their voice as well as an SM58.
The more directional a mic is, typically the stronger the proximity effect. Also proximity effect varies with distance between the source and mic.
Proximity Effect:
Notice the mic picks up more lows as the sound source is moved closer.
I suggest considering the proximity effect as a bonus feature, rather than a problem. In order to compensate for proximity effect, the audio tech will need to cut the lows and scoop out the low mids. By making these corrective EQ changes, the vocals sound natural and the mic is less sensitive to low frequency feedback and bleed from other instruments.
The EQ curve I use for vocals starts out something like this.
The low frequency cut balances out the proximity effect. Most of my experience is on Yamaha digital mixers. I typically configure the channel strip for 4 bands of parametric EQ with variable HPF.
Dialing in a good sound takes knowledge, skill, and practice.
The other things that have been mentioned are helpful as well. Band lay out is a relevant factor. But frequently bands center both the drums and lead vocalist. This pretty much aims the most sensitive part of the mic towards the drums. It can be beneficial to offset the vocalist to the left or right and aim the mic slightly away from the drums.
Specifically choosing the right equipment and using the right technique to reduce the acoustic volume of the drums is also an important factor. Many drummers refuse to believe they have any ability to play quietly, or they insist that drums have to be brutally loud in order to sound good.
Complete rubbish IMHO. I do agree that quieter drums will not create exactly the same effect as bashed drums, but IMHO that can still sound really good if the drummer knows what he/she is doing, chooses the right equipment, and works on the necessary control. But of course, part of the charm of playing drums is bashing...so good luck getting the desired change.
Drums shields can also make a pretty significant difference for the overall mic, but the drummer will probably hate the almost as much as playing with restraint. Also shields tend to be rather expensive and are a hassle to carry around and set up. For the record, I toured extensively and almost always used drum shields in smaller venues.
Maybe your audio tech is incompetent. But in truth, none of the factors you have discussed are necessarily within the audio techs control. All of these problems are within the bands control providing they are willing to actually makes the necessary changes. I suggest putting the blame where it actually belongs.
IMHO, the best solution is for the drummer to play quieter, and for the singer to stay right on top of the mic and sing louder. Adjusting the band layout, using a more directional vocal mic, and using drum shields should also make incremental improvements. There is no silver bullet unless you want to put the singer in a vocal booth on stage.
Good luck!
