On single instruments recorded with 1 mic there are no benefits to linear phase EQs. Phase is a relative impact parameter: it produces audible effects only when compared against something else with the same content. Record a guitar with 2 mic, flip the phase on one of them and hear for yourself.
We agree on that. Although not put in words in the question because if LEQs became the standard, single mic takes "wouldn't be harmed either".
Even on multimic'd instruments, the issue is not as likely to occur than one could think. Most of the time, different mics are there to play different roles so that they're set up to pick up different sounds.
That's true on the drum scenario you brought up. Consider now a string section recording, or an orchestral recording, or a chamber music recording, where mics are playing a bigger role that capturing very specific instruments and frequencies. Try using minimum phase eq differently on each mic, you'll notice very, very quickly!
Having said that, Sonar's Everything Equalizers free eBook  helped me get some facts straight:
Minimum phase EQs sound great in most instances, but during mastering or when applying delicate EQ adjustments to acoustic instruments it’s often best to use linear phase EQ plug-ins. Linear-phase EQs do not alter the phase of a signal, creating a more natural tonal effect and may also work well for parallel EQ duties. However, linear-phase EQs suffer from greater latency and high CPU usage, which means they can’t be used during tracking or in large, CPU intensive mixing sessions.
It is clear to me now that latency does become an issue, and so des CPU processing, if LEQ is used indiscriminately.
Linear phase EQs also introduce their own type of distortion called
pre-ringing, which some very picky people find offensive. In practice,
pre-ringing is rarely audible or much of a concern.
To better understand pre-ringing, I found this very useful video:
EQ: Linear Phase vs Minimum Phase by fabfilter
Quoting  again:
These equalizers avoid phase shift by analyzing the frequency content and applying gain with FIR filters, a process that takes a lot of time (latency). The processed audio is subsequently shifted earlier to try to keep everything in time. This time shift produces an audible echo, called a pre-ring, that immediately precedes sounds with strong transients, like drums. This pre-ring can smear or weaken the attack of drums and picked or plucked instruments. Getting back to the no free lunch idiom, linear phase equalizers trade phase shift for pre-ringing artifacts. We have now established that both minimum phase and linear phase equalizers have good and bad attributes.
On the use cases for LEQ:
For most applications of EQ, like sweetening instruments or mastering mixes, the actual phase shift is minimal because we use broad bandwidths and gentle boosts and cuts. For extremely narrow cuts or boosts, like when removing a resonant frequency from a snare drum, phase shift will drastically affect the frequencies surrounding the EQ’d frequency. In this case, linear phase EQ would be a wise choice and would remove the offending resonance without affecting the overall sound of the drum. Likewise, a steep high-pass filter that removes rumble from a vocal mic or guitar cabinet could wreak havoc on phase at frequencies well above the cutoff frequency. Phase shift artifacts may cause instruments to sound strange, so linear phase EQ would be a great choice. We can say that narrow cuts and boosts and steep bandpass filters are two situations where you might consider linear phase over minimum phase EQs.
Parallel processing instruments or subgroups in a mix would be another situation for linear phase EQ. Let’s say we have a vocal track and wish to duplicate the track and add some high-frequency shimmer by applying a high pass filter and compression to the duplicate (parallel) track. Minimum phase EQs, especially high pass filters, can induce phase shift that adversely affects the combination of the two tracks, causing unintended tonal changes. You can’t simply “flip the phase” and fix this problem. So, for parallel EQ duties, the linear phase EQ, with its lack of phase shift, may be our new best friend. You should audition both linear and minimum phase for parallel processing since in some cases you might find that phase artifacts sound interesting.
How about blending a top and bottom snare mic? For similar reasons to the above example, a linear phase high pass filter on the bottom snare mic (or hi-hat mic) may help retain the natural body of the snare while removing some low-frequency mud. The same goes for EQ’ing multi-miked guitar cabinets. For stereo miking, however, minimum phase EQ may be just fine since we are typically applying the same eq curve to both mics and both mics contain very similar source audio. Again, try both linear phase and minimum phase to hear what each does in your mix.
As of the latency:
Another consideration when deciding whether to use linear-phase EQ is latency and CPU power. Many linear phase equalizers load your CPU slightly more than traditional equalizers and all linear phase equalizers can impart extreme amounts of latency. Linear-phase EQ latency can range from around 3,000 samples to over 20,000 samples. At a 44.1kHz sample rate, that translates to between 100 milliseconds and more than half a second. While most DAWs provide plugin delay compensation, you may near the compensation limit once you exceed 10,000 samples. Pro Tools, for example, provides about 16,000 samples of delay compensation at a 44.1kHz sample rate.
Many modern plugin equalizers, like those from Izotope and Fabfilter, provide linear-phase, minimum-phase, and even mixed-phase modes. Mixed modes provide some benefits from each type of EQ. You should audition these modes on various sources to find the best uses of each type. Further, many equalizers provide resolution or quality settings to further optimize your preferences of sonic character vs latency.
Finally: should I use LEQ?
To answer the question of “Should I use linear phase EQ?” the answer is, as usual, it depends. Minimum phase equalizers, with their familiar personalities, would be my first choice most of the time. In certain situations, like narrow bells and steep filters, linear phase probably has the advantage. For parallel processing and multi-miked sources linear phase also probably comes out on top.
Some popular Linear Phase options:
- Blue Cat Liny EQ
- DMG EQUALITY
- Fabfilter Pro-Q3
- Izotope Ozone 9 or Neutron 3
- Logic Linear Phase EQ (Stock Logic Plugin)
- Melda MEqualizer LP
- Nugen SEQ-S
- T-RackS Linear Phase EQ
- Waves Linear Phase EQ