Appreciation without praise for a being is not deficient. In fact, that notion would be alien to me: most of the things I appreciate about the world don't directly have a creator in my worldview, yet I value them all the same.
I think you might be experiencing a problem with projecting a feeling onto other people that they may not share, and assuming they can't experience the same happiness as you do due to that feeling. Do you disagree that this might be the case?
Your premise is basically that "thanking God for a sunset is better than just finding value in a sunset," (just as an example), and having believed in God when I was younger, I've experienced both: I think the premise is false. My finding value in a sunset or anything else that (in my worldview) doesn't have some being as a creator brings me just as much happiness as when I believed it did have a creator.
So I've experienced both. Perhaps you have always believed in God and have never experienced appreciation that isn't the context of thankfulness. Perhaps I can't convince you that it causes just as much happiness, but perhaps you can take my word for it (since it's my introspection to have) that it does.
No, I've made the opposite journey and so have experienced both also.
There's no argument to be made "from happiness" and in fact I should abandon any wish to convince anyone of anything religious or non-religious, because worse than a sales-man, I'm sure I find ways to put people off!
It's an interesting point in itself though, to do with appreciation.
I enjoyed many a landscape without requiring contemplation of being behind it, but yes, I do see belief as providing an extra enhancement. How so?
You still have the same view, but there are two liberations:
1. When I say, What a beautiful view! I am giving praise, and I do believe that praise - by its nature - is relational. We can continue without making it so, but, in my opinion, something would be missing, which truely connects a person to nature. Again, I know, everyone can chime in, No! I am so intimately connected to nature, and I don't need God - so beit, people are entitled to their opinion - but in my opinion, something is lacking, and that lack will inevitably evolve into a kind of pagan worship, whereby the person does seek a subject in what they are connecting with - because it is different that just a wall - and they will start talking about Mother Nature, and some such. (Okay, as metaphor, perhaps - but people start to believe it really has will of its own! So Basically subverted God-need).
If they don't do that, then it makes the "connection" somewhat hollow - because gramatically, we can see, connection involves two subjects.
I can't connect, in a human sense, to a bottle of water. So why do people talk about nature in the same way?
2. It liberates me from seeking in nature what nature is unable to provide - namely, as above - anything at all. God provides, because God is a subject - gramatically, whether you believe or not -; a person provides; these can have intention. But nature cannot provide, except, again in a metaphorical sense, as an extention of another will. God provides me with apples, through the tree. It's a technical point about language, but it is very revealing.
People will believe what they want to believe and I make no claims on anyone else's heart or mind.
If we think about Art, one of the reasons people love art is this sense of being spoken to by an artist, and it is the reason why a mona lisa painted by a robot, apart from being a curiosity, would not really be of great interest to people. This should say something about what connection and appreciation of beauty amounts to, imho!