Cast shileleagh every round outside combat. It will always be up with 9 rounds renaing on its duration.
I think a lot of people Nova from the sound of it. If you're using spiritual weapon and guardians your going to be out if spells very quickly.
Spells with duration like that tend to be an efficient use of spell slots. Two spell slots per encounter isn't that much of a nova. We're talking roughly 8-10th level given the feats and ability scores discussed and that gives room to do both 4 or 5 encounters of the day. Healing might dip into it but that just means swapping out guardians for bless a couple of times. It doesn't have to be all encounters either. In a level range where the character has 12-15 spell slots and the standard expectation is 6-8 encounters per day then 1-2 spells per encounter is pretty typical. That's rationing it instead of going nova.
The competition for shillelagh comes from spiritual weapon, which is hard to give up unless a person has big plans for that bonus action. Casting shillelagh would cost that one attack.
Constantly casting shillelagh carries similar issues to constantly casting guidance. It's hard to be stealthy when one of the party members won't shut up and keeps casting spells and impacts stealth and surprise. Walking through towns and in social encounters someone constantly casting magical spells is going to be viewed with suspicion at the very least and quite possibly open hostility.
I would also point out again (if it wasn't clear) that using shillelagh with a domain that gives potent spellcasting instead of divine strike is using a melee attack that gives up damage. Those cleric domains would be better off looking at attack cantrips over weapon attacks, outside of the possible arcana outlier. Using a spellcasting ability score for attack and damage doesn't offset the bonus damage from divine strike even if there is a small gap between the two ability scores.
There is an error in your OP as well.
The Nature cleric can cast chillagh since it picks up a Druid cantrip. You can wear medium armor, soak up 1 less AC and similar to things like light and arcana clerics you can key everything off wisdom including your melee attacks. This matters latter on where the "melee" cleric should be using spiritual guardians, clerics that don;t basically stink at melee. This is also why I think nature clerics are better at melee than things like war and tempest clerics. The way a staff+ shillelagh interacts with polearm master is also funny. If you want a beat down cleric that is good at spells and spell buffing play a nature cleric in medium armor.
Nature clerics gain heavy armor proficiency as a bonus at 1st level.
PHBpg62 said:[FONT=Verdana,Arial,Tahoma,Calibri,Geneva,sans-serif]Acolyte of Nature
At 1st level, you learn one druid cantrip of your choice. You also gain proficiency in one of the following skills of your choice: Animal Handling, Nature, or Survival.
Bonus Proficiency
Also at 1st level, you gain proficiency with heavy armor.
Taking PAM and shillelagh seems okay because PAM is competing with spiritual weapon for that bonus action anyway, but casting shillelagh would still cost a bonus action attack. It this case it's at least not costing a feat/ASI so the tradeoff isn't so bad. PAM doesn't scale up in damage through spell slots like spiritual weapon, but it also doesn't cost spell slots and it increases the chance of landing divine strike.
Or you could just take HAM, start with a 16 STR and 16 WIS, and fill the bonus action with spiritual weapon. Or numerous other useful feats.
It's hard to argue variant human power gamers use shillelagh on clerics.