I mean, just because you have spirit guardians doesn't mean you have to use it. If you're a support-focused cleric you might prefer to concentrate on, say, Slow (which Order Clerics get), or even just Bless. The problem with multiclassing as a support Paladin to up your spell slots is that you really want Paladin 6 for the aura, and then if you multiclass into a full caster (Divine Soul Sorcerer, say), it's level 11 before you get 3rd level spells, which is two levels later than a single classed Paladin (although you do have a lot more slots to use). Plus, Lay on Hands scales with Paladin level, so if you're multiclassing you give up the healing advantage you have over the Cleric.
Compare an Cleric 6 to a Paladin 6. The Order Cleric has 4/3/3 in spell slots; the Paladin has 4/2. If the cleric uses one 3rd level cure wounds and one 2nd level cure wounds, that heals an average of about 30HP (assuming 18 WIS), the same as the Paladin's entire lay on hands pool. And the cleric is still up two 3rd level spell slots (and gets two channel divinities per short rest vs the Paladin's 1).
Granted, the passive aura is hard to beat, and the Cleric's 3rd level support spell options are not that great, though again, Order Clerics get Slow, which is pretty nice (War Clerics get Crusader's Mantle if you wanted to be more Paladin-y; their 6th level Channel Divinity option is nice too, though their other domain features are not very support-oriented).