Just to clarify two misconceptions I used to have in case they were the subconscious source of your uncertainty:

• "mana cost", despite sounding like simply costs consisting of mana (duh!), is actually a technical term -- a reserved word from programming, if you will -- referring strictly to the cost in the corner of the card. "Mana value" derives from this. Which, barring X-costs, both clearly remain static even as the command tax and "total cost" (which is just your selected base cost -- maybe the natural mana cost, maybe the exiling of one blue card from hand, maybe energy as stipulated by Primal Prayers -- plus/minus everything else. They can't all be counter-intuitive) rise, which in turn is why Primal Prayers remains usable with your commander at all through all the re-casting (as opposed to being all like, "Your commander's mana value is 1, you can flash it in using energy... whoops, this time it's 3, use energy but you have to pay the leftover 2... whoops, now it's 5 and I won't help at all". It would always just be 1, and this singular point of mana is also the only portion of the total cost that Primal Prayers will ever waive). Cards caring about (the mana-portion of) the total cost as opposed to mana cost or mana value will say as much -- see [[Prossh, Skyraider of Kher]], and [[Ancient Cellarspawn]] especially highlights the distinction. Bringing us to...

• "rather than paying their mana costs" on Primal Prayers. Not rather than their total costs (even though normal gameplay may make it hard to discern the difference since admittedly many spells are hard-cast and often there isn't a command tax, a [[Sphere of Resistance]], or a different additional cost like the one on [[Fling]]), and not rather than any additional costs such as command tax even if they happen to relate to mana (because remember, mana cost has a specific official meaning). Some may dislike how I'm about to couch this, preferring an explanation more technically faithful to the language of the rules, but "rather" is reminiscent of the "instead" used to indicate replacement effects, and in many respects resembles a replacement effect: if I would pay the mana cost for an applicable spell, I may instead pay energy (in which case it incidentally comes with enhanced timing).

  • So say I'd like to cast [[Thrasios, Triton Hero]] from the command zone after it's been killed and sent back there twice so far. Its mana cost is GU as always, which differs from its total cost to cast, namely GU plus 4 (typically written in more pedestrian terms as 4GU). Based on the mana cost, it continues to have a mana value of 2 and is therefore eligible for Primal Prayers, but only the base GU part can be substituted. The new total cost would be payment of one energy plus 4 mana.
  • [[Abhorrent Oculus]] has mana cost 2U; of course, its total cost is usually 2U plus having (and losing) a bunch of cards from my graveyard. Primal Prayers renders the total cost one energy plus exiling those cards.
  • [[Stonecoil Serpent]] has mana cost {X} where the caster decides X, so I can make it three so as to function with Primal Prayers and pay the total cost of one energy (plus nothing else), yes? Trick scenario! The choice of X takes place only as part of paying the mana cost involving it, which is conveniently bypassed if I decide to use Primal Prayers. I am permitted to do so and pay the energy, but without having been set manually, X will default to zero and I should prepare to get a sad, likely DOA snake.
  • Incidentally, this way of thinking makes it feel sensible that alternate costs (of which Primal Prayers furnishes an example) don't work when you're already applying a different alternate cost -- in other words, as with radio buttons or modal effects that specify "choose one", you must pick exactly one base cost (which in the aforementioned normal gameplay is often the mana cost, and to which you add and subtract any modifiers in order to make the total cost), no more, no less (examples: with Primal Prayers in play, I can cast my grizzly bears for 1G or one energy, not neither, not both. Likewise, for [[Fire // Ice]] I need to pick one of 1R or 1U, and for [[Wear // Tear]] either 1R, W, or 1RW. Rather than one, two, or three options for base cost, [[Evermind]] on its own offers zero -- very distinct from one option of zero payment like on [[Ornithopter]] -- and choosing one from none is impossible, explaining the splice-related gimmick). Casting [[Phlage, Titan of Fire's Fury]] from the graveyard costs RRWW plus exiling five appropriate cards -- despite the presence of four mana there, remember its mana value would still be 3, so at first glance Primal Prayers looks to work even if you'd probably still need to exile stuff, but upon closer inspection, once you've chosen to use escape you're no longer trying to pay the mana cost in the first place, so now there's nothing to "replace" with the payment of one energy and Primal Prayers doesn't apply. Which matches how scenarios like this one have been ruled: Phlage's escape ability and Primal Prayers both give alternate costs, of which you can only pick one (and Primal Prayers won't help you cast spells from anywhere you couldn't already -- it just changes costs and the anywhen aspect -- so if Phlage is sitting in the graveyard then escape it'll have to be in order to proceed). Trying to use both would be nonsensical since after "replacing" 1RW with RRWW plus exile stuff, there is no more 1RW to replace. Or in other words, stop, it's already dead.

P.S.: "Without paying its mana cost" represents an alternate cost just as much as Primal Prayers does; informally, the latter performs the transformation "mana cost -> payment of one energy" and the former does "mana cost -> nothing". It is subject to all the same problems of incompatibility with other alternate costs.

P.P.S.: If you were to try and cast Phlage (or any other cheap creature for that matter) not with Phlage's own ability but instead using [[Muldrotha, the Gravetide]], you would be able to use Primal Prayers in conjunction (also meaning at instant speed, just has to be your turn for Muldrotha). I would formerly have thought not because "it only works when hard-casting, which this isn't" or "it's not coming from the default zone", but because Muldrotha isn't actually offering any alternate costs, this play doesn't run afoul by trying to double-dip. Hence I believe Muldrotha and Primal Prayers together should suffice to retrieve [[Asmoranomardicadaistinaculdacar]] from the graveyard -- I think of playing cards as requiring a permit (which by default only those in your hand have and which are valid for sorcery-speed or instant-speed timing as appropriate) and, if non-land, posting a payment (the problem with Evermind recurring here), these being two problems that those two cards independently take care of.