There's a difference between soft power and clerical power. Assume for a moment that gods only have so much magic they can hand out; in my world it roughly corresponds to the number of worshippers. So a priest is working to support their god by leading an example, bringing people to the faith. The work they do is no more or less important.That's very true, and I'd venture a guess that's how most players have always thought about it over the years. To me though it still feels artificial and implausible merely because of how fast character can (and oftentimes do) go from "powerless" to "superpowered".
In the case of your dwarf... they were a priest for 100+ years getting nothing whatsoever in terms of power (whether that be spells or fighting skill or health etc.). But then for whatever reason they acquire those abilities because they become an "adventurer"-- they go traipsing through a series of caves killing a bunch of rats and wolves-- and now suddenly not only do they now have all this new power, that power essentially begins increasing massively over a matter of hours, days, and weeks. 100 years of leading prayers and doing research and helping townsfolk and healing the sick in the clanhold gives them nothing... but becoming an adventurer and killing a bunch of wild animals and maybe a couple goblins and they're suddenly superpowered compared to everyone else around them.
That's the kind of thing that I see as illogical story progression and why I choose not to use the game mechanics of leveling to indicate anything about who characters are and what characters have done in the past. It just doesn't make any sense.
So becoming a cleric can be a reward or it can be a necessity. This priest has brought in (or retained) many followers for years. He has served his god well, just not on the front lines. I mean, who is more important. The pilot flying a jet? All the people that support and maintain the jet? In this case the priest is the maintenance crew while the cleric is the pilot. That doesn't make the maintenance crew less important. A maintenance guy being given the opportunity doesn't suddenly become an ace pilot just because he knows how to maintain the engines. It's simply a different skillset.
In addition my campaigns span years because PCs regularly have months of downtime between adventures. Like professional athletes, they don't get the skill from the game per se it's the training between the games that matter. They learn from their games but they actually improve skills during downtime.
Or, just ignore it all. It's just a game and it doesn't have to be logical to be enjoyable.