The nature cleric can skip magic initiate and takes PAM.
The others will skip it, maybe take it later or take a different feat.
A level 1 PAM nature cleric in medium armor isn't a bad deal. I would probably take warcaster over asi if I was planning on using spiritual guardians melee build.
The 3 builds.
Nature cleric, PAM lvl 1.
Arcana cleric. Magic initiate, GFB.
Every other type of cleric
Magic initiate.
All will probably take warcaster lvl 4 or 8.
As previous poster stated only arcane cleric can get gfb keyed off wisdom. At level 8 they can double stack their wisdom modifier on it.
I have also seen war, tempest, death, life clerics in action. None of them impressed me in melee, the light cleric was good at being a spellcaster.
Also what if you're not picking the best domains? My magic initiate trickster or knowledge cleric would work alright yes?
Standard spread isn't typical of an optimization discussion, but even so you are back to most clerics taking shillelagh at 1st level via feat, war caster before 10th level, and an 18 WIS at best. Shillelagh doesn't help someone who isn't pumping their casting stat over feats. That would be shillelagh with an 18 WIS, no damage for WIS bonus unless specifically arcana using green-flame blade, or divine strike avg 4.5 damage per hit because it's independent of WIS and beating the arcana cleric's 18 WIS or 20 WIS lacking a feat. If the cleric is taking mostly spells that don't require saves or attack rolls (like combat buffs and healing) because he or she is focusing on melee then WIS becomes the secondary ability score.
An 8th level STR / WIS cleric can easily have 18 STR and 16 WIS on a standard point spread plus a feat. Or vice versa. The trickster cleric in your example on a standard spread looks something like this:
12 STR
14 DEX
14 CON
8 INT
18 WIS
10 CHA
That's taking shillelagh through initiate at 1st level and war caster at 4th or 8th level. Compare that to the same character who takes heavy armor proficiency at 1st level instead of shillelagh.
18 STR
8 DEX
15 CON
10 INT
15 WIS
12 CHA
That's taking resilient con instead of war caster at 4th level for better stat spread. That could be three 16's instead or wait for 12th level. Shillelagh isn't giving an stat advantage on the attack ability score. It does give an advantage on spells that require saves or attack rolls keeping in mind you just made a cleric who attacks via melee as his standard attack. My example isn't optimized either, still caps at 20 main ability score with two 16's and can add another feat or bump up to an 18 WIS or 18 CON instead of a feat.
It seems counter-intuitive to go STR and heavy armor on a trickery cleric but if a person wants to melee the armor helps, the strength is important because of the STR 15 minimum goal anyway, and investing in strength already means continuing to do so isn't a big deal and strength covers what shillelagh would already.
Trickery cleric is already counter intuitive giving no proficiency bonuses but divine strikes (using poison as a damage type) instead of potent spellcasting. If I were playing a trickery cleric I might focus on DEX / WIS for skill benefits and wouldn't need the heavier armor or shillelagh. Shillelagh might be tempting if forgoing DEX or STR advancement on this one but it's not going to make much improvement in combat damage. Building for STR and fitting in PAM and GWM with a focus on buffs / healing would be much more impressive and is doable. It doesn't take capped out STR with those feats to beat shillelagh and max WIS.
Nature is a bit different because they don't need to spend a feat for shillelagh and get divine strike instead of potent spellcasting, so sure, take it. It's a cheap basic combat improvement. There are more damaging options but for the cost there it's reasonable enough.
Knowledge gets potent spellcasting instead of divine strike. Use word of radiance.
Any 8th level cleric with Potent Spellcasting and a wisdom of 20: Get surrounded by 8 enemies then spam Word of Radiance. Average damage = 96 hp per round.
Just an example, but any domain with Potent Spellcasting, including Arcana, is probably better off not wasting time hitting things with a stick. And Arcana has lots of other good options for its two wizard cantrips competing with GFB and BB.
Word of Radiance specifies targets that you can see. You wouldn't get all 8 surrounding you unless you have eyes in the back of your head. And eye slots in the back of your helmet to match. I guess if the cleric can jump high and look down shenanigans. I'd require a DEX (acrobatics) check to flip and cast during the jump in order to look and cast from the right angle during the jump, but that's just me. If the character can jump well enough over a crowd he or she might be able to see 9 targets. It's easier with flight. Three dimensional combat FTW. Also, I might try things like that during combat. ;-)
Sword burst isn't selective but it does get everyone around the caster so would catch twice as many targets as word of radiance, and is easily available to arcana clerics.