I'm not sure I'd like that as a player, and I probably wouldn't personally do that in DM, in 4e, or any other D&D version.
For me, one of the big issues with that is: If any character can use a Religion check to pray for a miracle, why would they do anything else?
Well, tehnically speaking, in 4th at least, they did. The same stats that powered your skills were the same stats that powered your abilities. So shooting a magic missile with your int score is basically using your arcana skill to shoot magic missile. The difference between "paying for a miracle" or "doing magic" using your skills and using, in 4th's case, a power or spell is that the codified spell is, or can be thought of, praying for a
specific miracle that your god has set out certain parameters for you to be able to achieve. Want to shoot a bolt of holy energy into your enemy's face? D20+stat vs enemy defenses. Want to bring your friend back from death? Well that's a little bit more subjective.
"Pray for a miracle" or "Perform a feat of magic" has a virtually unlimited possibility space. Presuming that this extends to things like being able to use Nature to supernaturally manipulate the natural world (cause plants to grow or whither, rivers to lower, skies to clear, remove toxins from a thing, etc.), and possibly other skills (can Insight read minds like a telepath? Can Persuade duplicate charm effects?), this makes selecting a skill largely a superfluous process. Every character just has one "Do Almost Anything" skill (whatever that skill might be), and can use it to do almost anything. The difference between saying "I roll Religion and pray for a miracle!" or "I roll Arcana and harness arcane forces!" is simply one of set dressing, without mechanical distinction. Mechanically, why not just say, "Here's your 1-20 chance to Do Whatever, roll the dice and tell me what you do?"
Sure, but that's a sign of bad DMing if a DM just lets you "do whatever" with "any skill". A good DM sets the bars on what you can, or cannot do with your skills and then tells you how high you have to jump in order to do what you want to do within those skills. I think that's great about 5th's somewhat
less codified system. You really could do almost anything with your skills! Which I think allows players to get really creative with what they want to do and how they go about it because there isn't a pre-defined set of brackets limiting what you can do with them.
It also seems an odd fit for a skill system in a game with levels, where the suggestion is that one "gets better" at the skill as the modifier increases, and the sense that one "gets better" about wishing for miracles is a fairly counter-intuitive one. Miracles in narrative don't seem to conform to the idea that one can "fail to pray hard." It's simply a decision on the part of the miracle-granter.
I disagree completely. You can certainly "get better" at praying, just as you can "get better" at doing anything. While at the end of the day, yes, the final decision is more or less at the whimsy of your god, not all gods are capricious, two-faced jerkwads. Some of them have very clear likes and dislikes, clear foes, clear allies, clear wants and needs. For those gods, it's a relatively simple process to become more favored with the god. Kill their foes. Help their friends. Follow their rules and laws. It's basically been true since the dawn of religion that the more you do things your god likes, the more your god is willing to do for you. Now this isn't always represented by leveling up, but it can be, and if you're including such things as using your religion skill to pray for miracles, it is on the DM to enforce these sort of things that aren't explicitly written in the rules. Leveling up your character is just a representation of your skill in your chosen profession. A higher-level cleric should be more in touch with the will of his deity, but maybe not, maybe he hasn't taken the time to really get to know his deity and is just more adept at channeling the power his deity sets out for him. Once again, if the DM is allowing things like "use skills to make magic" the DM needs to take more into account for the DC of that miracle check than just class level.
I'd lastly worry a bit (but only a bit) about stealing the thunder of any actual divinely-inspired characters. If the party Druid is better at getting miracles from gods she doesn't even worship than my devout fighter just because she's got a better Wisdom and training in Religion, that's not going to be something I'm going to like.
I'd agree with this. Perhaps if the fighter is not the religious sort, he should try to convince the party druid to pray for the miracle instead. Perhaps because the druid worships a different god, that is who the druid must appease instead of whomever the fighter was planning on praying to. A really good diplomacy/persuasion check on the druid might make the druid willing to help.
Since I like my set dressing to have a mechanical effect that aligns with the story we're telling, these would not be results I'd struggle with when playing in or DMing with such a system. Which isn't to say that these are inevitable problems at every table, of course.
Well you're always welcome to play and run the way you want, though I do think a little creative thinking with skills goes a long way in this looser edition.