There is multi-fold reasoning behind this and it has little to do with their actual mechanics--it's more a matter of perception. If you read to the end of the second sentence you quoted from PHBII...
Many players prefer to go for the spotlight with a fighter or wizard (or the equivalent) rather than playing what they see as a supporting character.
Emphasis Mine from PHBII 155
As to how this perception works, in my experience running games for players from veterans to newcomers...
Perceived Obligation to Have One
Clerics are, as a general rule across editions, the best source of magical healing around. Thus, a typical party feels obligated to have a Cleric. This is true even into today where I see regular discussions about "Okay, we need a Cleric...who's going to play it." Even as a DM, I've had to step in and go "guys, you don't need a Cleric."
As a rule in dealing with human psychology, when something is required it becomes less desirable. It is a perceived loss of freedom. In D&D, it means that in the party, somebody has to play the Cleric...so somebody has to set aside the character they wanted to play so that the party has that necessary Cleric.
Perception as "The Healer"
Clerics are masters of divine magic, which is
especially good at healing.
-Players Handbook 3.5E
Look at any MMORPG in the world and you can see that Healers are rare. Queue up for random dungeons in World of Warcraft as a Healer, and you can get a group practically instantaneously while all the DPSers have to sit and wait.
Because Clerics are generally the best at Healing, they are often perceived as a dedicated healer. I still run into this today when introducing new players to D&D and they recoil from the idea of playing the Cleric because they "Don't want to just stand around and heal all the time, that's boring."
And this isn't unique to new players...I've had to explicitly spell out the actual effectiveness of Clerics in roles other than Healing to veteran D&D players before they could get past their preconceptions about the class.
Because Clerics are presented as 'Support Casters.'
AD&D 2E calls this out...
Spells are the main tools of the Cleric, however, helping him to serve, fortify, protect, and revitalize those under his care
-AD&D2E Player's Handbook
A Fighter is a straightforward contributor...they rush to the front of the battle and engage directly with the enemy. A Wizard is a straightforward contributor, they Fireball and Meteor Swarm and lay waste to the battlefield. Yes, there are other, more subtle ways to play a Wizard, but the simple and obvious option is there.
Clerics have some directly offensive spells, but they are mostly focused on buffs and heals...and their direct offensive spells tend to be weaker than comparable offensive spells from other classes. As a result, the Cleric appears to be a PC Class that is focused on making other PC Classes succeed. While the truth of the matter can be quite different, that is a perception that is less than desirable for your average player. (Again: see the ratio of DPS players to Healers and Tanks in any MMORPG)
It feels good to drop big piles of dice worth of damage. It feels good to be the one going toe to toe with a dragon. These are straight-forward, clearly meaningful contributions to the party. A Support Caster's contributions aren't as plainly obvious...they prevent friends from dying, make friends hit harder, and so on. Again, this is not the only way to play a Cleric, but it is how they have largely been presented in the official material.
Clerics are not presented in a way that makes them look Directly Powerful
A Cleric's magical ability to destroy stuff is not necessarily straight forward. As was mentioned in this answer, it takes a greater degree of mastery and expertise (or luck) to draw out the merits of certain classes. In short: the ol' CoDzilla is not an obvious solution. You don't look at the basic presentation of a Cleric in rulebook materials and immediately say "Wow, this guy is massively overpowered!" You have to sit down and think and look at the character's abilities, study their features and spells, not get intimidated by the vast array of options, and realize what they are capable of when you do things in the right way. Of course, as was mentioned in the linked question, it's entirely possible to trip over this power while playing a Cleric, or to discover it while digging into the class. But that's really not the sense you are given by the rulebook write-ups on the class. They are treated as "a caster who supports their allies."
'Tier' does not necessarily equate to popularity. It speaks of an optimized character created by someone with the willingness and focus to dig deep into a character's capabilities to bring out their best features.
As a result of all of this...
Clerics don't feel like "The Hero" to a lot of players.
Heroes are the ones who directly fight and defeat monsters. Look at novels, legends, and film. The Hero is the mighty wielder of arcane power who levels powerful magic to destroy their foes, or the skilled swordsman who slays dragons with naught but his wits and his blade, or the crafty rogue who outsmarts his foes and then destroys them. You don't find support casters as the main characters of these stories.
If there is a Healer, they're basically an NPC who exists to patch the hero up after their "mighty duel." Support Casters exist to make the Hero strong enough to win the battle. This perception carries through into D&D for a lot of players (including many that I have introduced to the game). They are playing D&D to be a Hero...not the NPC that helps the Hero.
The designers were clearly aware of this, and were acknowledging that is the prime reason that a party may lack a divine caster. The way a Cleric is presented tends to breed a perception that they are this 'Supporting Character.'
