I can totally relate to your dilemma from personal experience. Let me share my thoughts based on my own experience as the primary vocalist in the bands I have been a part of.
It is vitally important that someone in the band (either the lead singer or another band member) can actually sing any song that the band plays - in the key that it is played in. Most singers have a limited range which would preclude certain songs in particular keys.
As a group, a cover band needs to agree on what songs they want to cover in their repertoire. Things that feed into those decisions will be the personal musical taste of the band members, the musical taste of the target audience the band will perform for, and the musical ability of the musicians.
Most cover bands will stay within a particular genre or genres that the instrumentation lends itself to. For example a bluegrass band would likely have a "fiddle", a mandolin, perhaps a dobro, and an acoustic flat top guitar and maybe an upright bass. A rock band would probably have a couple of electric guitars, electric bass guitar and drums. Jazz band might add some horns and electric piano.
The bands I have played in did "classic rock" and "country" featuring acoustic guitar, electric guitar, electric bass, drums and sometimes harmonica.
In all of the bands I played in, I was the "lead singer" on most songs but other band members sang harmony and there were certain songs outside my vocal range that other band members would sing lead on. Spreading the vocals among various band members allows for greater flexibility in terms of key selection as well as prevents the lead singer from becoming hoarse by the end of a 3 hour gig.
Every band I have performed with consisted of musicians who were capable of playing any given song in more than one key. The band would decide what key to play a particular song in based on the vocal range of whomever was going to sing that song.
Many songs feature signature guitar licks that are required to give authenticity and recognizability to the song. Some of those licks are easier to play (or better match the familiar recording) with the use of some open strings. In those situations, the key can be altered by using a capo on the guitar that will play those particular licks - thereby allowing the licks to be played in the new key - the same way they are played in standard tuning in the original key. On some songs one guitarist might play in the key of E for example while another uses a Capo on the 2nd fret and plays chords from the key of D to match the guitar playing in the key of E. The Capo Key Chart below might be very helpful to you if any of the guitar players in your band would consider using a capo to alter the key. Bass players can generally play in any key with no problem since they don't have to worry about chords that don't work well on guitar in certain keys.
Another thing that I have done when performing is to tune all the instruments a half step flat because many of the songs we cover strain the upper limits of my vocal range in standard tuning. Also, many original artists routinely recorded and performed with guitars tuned half step flat. You would be surprised how much a half step (one semitone lower) will make in hitting the high notes in certain songs. I have a list of songs that I can only sing if tuned half step flat and I like to group those into one of the three sets. So perhaps the first two sets are in standard tuning and during the break between the second and final set, all guitars and bass are tuned down a half step for the final set.
One final option that I can offer is if a song is too high or low for you to sing in the key the band insists upon playing the song in, try singing it an octave higher or an octave lower as the situation dictates. While the vocals won't sound exactly like the record, the instrumentals will, and most times the audience will still enjoy the song. You could also try a vocal processor that can alter the pitch by up to an octave in either direction. So for example - you sing in the C4 range but the PA renders the vocals to the audience in C5 (an octave higher) or C3.
Hopefully at least one of the ideas presented above will help you and your band mates find a solution that allows everyone to agree on an approach that allows for an acceptable and achievable performance of all the songs the band wants to incorporate into their repertoire.
Have fun sharing your music and be safe out there.