You are lowering the performance of the $200 rifle?
Yes. The scope is the aiming mechanism of the rifle. See my photos provided above. When a shooter can’t find the edges or center of a target because their scope offers aberration or lacking resolution, they can’t aim consistently, and performance suffers - as measured by rounds on target, game taken, and group size. If you can’t see it, you can’t hit it.
As a parallel, an aphorism in photography is “date the body, marry the lens.” This is said to new photographers to remind them, succinctly, that glass matters much more than the body, and while body performance will change rapidly in time, relatively, good glass prevails. Exactly akin to your analogy of a $3000 scope on a $200 rifle, which you wrongfully assumed would be an absurdism, sticking a flagship lens like Canon EF 70-200 f/2.8L III in front of a Canon Rebel T6i, an entry level, 10yr old camera, will give drastically better results than sticking a $150 kit lens EF-S 75-300mm f/4-5.6 STM in front of a $2500 Canon R6. Both the body and lens obviously matter, and certain genres of photography, like sports, are exceptionally demanding of the camera body, but the glass is what we see, and we can’t do anything to get around that.
So yeah, if I had the choice of shooting a Savage Axis Precision with a Tangent Theta or an Impact Precision with a Vortex Strike Eagle, I’d take the Axis with the Tangent Theta every time…
And you don't have place holder scopes laying around already? I find that hard to believe. I always have one or two sitting around. I guess it's possible your place holders may be busy already.
I am “scope poor” most of the time, so when I get a new rifle, I need a scope too - I don’t keep scopes just sitting around. I buy scopes to saddle onto rifles for certain applications, and typically, if I try a scope and find I don’t have use for it, I resell it. I’m more apt to take a good scope off of a rifle and rezero it onto something new, even for a short time, than to buy a lower grade scope than I’d actually want just to have it lay around waiting for a rifle to mount. That paradigm has always seemed like an insecure sorority girl to me - always with some guy, wasting energy even if they don’t actually like them, and in fact, knowing they don’t actually like most of the dudes most of the time, just to have a guy on their arm.
When I try a new rifle, usually I have the scope bought before I get all of the parts for the rifle, but otherwise, I pull a scope from another rifle - usually one of my SigSauer Tango4 4-16x scopes from my hunting rifles or I pull one of my Bushnell DMR II’s from my plinking rifles.