Yes, most linear phase plugins are CPU hogs. Some fare better than others, but in general.... they tax the CPU.
To answer the question about why you would bother with using one.... it entirely depends on what you are trying to accomplish. Linear phase processing has a specific "purpose".
A regular EQ has some degree of phase shift. If your trying to EQ out an individual guitar track.... this isnt a problem. But sometimes that phase shift IS problematic. There are lots of youtube examples with folks actually measuring the degree of phase shift, and what sort of issues this could cause in certain situations.
I'll give you one practical example where I would employ a linear phase EQ. Say the bass guitar track needs to have some more edge so that it comes forward more in the mix. The "sub" content is fine. I dont want to simply turn the bass up. I just want the attack to come through a little better.
What I will often do is duplicate the bass track. Leave the original "as is" in both volume and whatever general processing i've done.
The duplicate track I will send through a guitar amp sim and add a little gain/distortion to it. I can then blend this in to taste with the original bass track just to get some grit and presence to come out.
BUT... I dont want to stack bass on top of more bass. Remember I'm only looking for some additional presence and cut with this duped bass track, so with that duplicate track that I intend to distort, I will do a hi pass filter(this is where the eq comes into play) around maybe 150 to 200 Hz to get rid of the sub stuff(the original bass track is carrying that just fine).
The act of applying a hi pass filter to that bass track is going to cause some phase shift with a conventional EQ. Not an issue by itself, but when blended with the original source bass... this is where the phase shift can cause some issue. You could experience a degree of phase cancellation at certain frequencies between the two tracks when blended together.
A linear phase EQ is going to attempt to avoid any phase shift, and ultimately there is less worry about any out of phase issues in an example like this where your blending two tracks based off of the same waveform.
I would use LP EQ in a parallel compression application as well if EQ is necessary
The transparent nature of these types of EQ's make them nice for an overall mix EQ also.
I avoid the CPU hit by simply freezing the track after Im done tweaking the EQ