The 70-300 isn’t a $2000 lens but it’s a good Allrounder lens. I use this lens on d7000 and d810. The 810 have a stronger focus system.
Still I get the same quality on pics on both cameras just have to more cautious on the 7000.
In the old days a 300 mm lens was 300 mm long same with other focal length. And sure between the 70-300 and the 70-200(got it to try) are quite different when you look through the viewfinder. Wish one is the true about the focal lens I have no idea..... I just don’t worry about it......just saying

My first iPhone6 with 16GB where already about the half was gone just for ISO. iTunes wiped out one time my hole phone. The best two options I found without iCloud and what ever.....
https://www.wideanglesoftware.com/touchcopy/?matchtype=b&keyword=touchcopy&gclid=EAIaIQobChMIv7OssZ3Q3wIVAaeGCh1eJg82EAAYASAAEgKyxvD_BwE

And the sandisk iXpand flash drive.

I'm shooting for a companie and we use the nikon D90 and later on we changed to something newer. After month later someone gave me the D90 again and after the first pics I took I zoomed in 100%, could not see if my pics was sharp......Know the bad thing on Focusing, we push a button and the focus should be correct what isn't allaway the case. It does matter what length of lens you use, Time aperture, ISO, camera shake, movement of the subject, Focus point.....Some cameras and or lenses have problems with black or white, just try on a black monitor.....Focusing is a learning process.....My first DSLR I hated the autofocus vs. my old manual camera- split screen focus manuel. I had to learn focusing and this was frustrating....

not all D lenses have build in focus engine what makes the focus slower and miss focus on the D7000. On the D810 is it better.....

separation between metering and focusing makes a difference. My first DSLR didn't have it separated and I wasn't often sure if I focus right.

Rest the hole camera, software update can also help. I would check how many shutter clicks is on the camera. After a certain amount of use some cameras are just not worth to fix it at all.

Did you consider the 6D series or 7d series or even the 5d series.....just asking....

I shoot with the first canon DSLR with a tampon 75-300 5.6... little league baseball and some other sports inside. The pics wasn’t the best quality( lots of grain) but still they ware good enough that parents liked them and bought them.
My advice is check the highest ISO, if it’s to grainy than lower the ISO step by step. TV and or M is your best bet. Just push this camera.....
The best pics I got wasn’t at the game time, it was through “exercises time.
I don’t how canon is with older lenses but with Nikon I can use older lenses (I have a pull and bush 2.8) for $180...just saying

Where can we see your Images?

Try a different pawn shop, if you don’t like what they offer you don’t have to sell it.

You have dual memory slots, set one for jpg and one for raw but I’m not sure if this speeds up the buffer. The read and write speed of the memory card plays definitely a role, too. Check if you have a setting what makes the camera slow (I reset my d7000 because some errors)
The focus engine isn’t the strongest and fastest ether. 70-300 VR 3.5-5.6 on the d810 vs d7000 shows difference in speed and sound. My old high end lens 18-55mm2.8 lens I don’t feel this kind of a different.

From the d7000 to d810 what a difference. I have an older DX 2.8 18-55mm it’s a beauty-on any camera. I wanted a quick, cheap FX lens so I decided for a 28-80 3.3-5.6 G.....lol......sure it’s 100% plastic but it works great what I can’t always say about “better Nikon glass”....still looking for my next beauty glass

😂😂😂

Be aware of how many models exist, not every model is nice and every camera body acting different to different lenses. Just Compare the 50 mm https://kenrockwell.com/canon/comparisons/50mm-lenses.htm

I use the 18-55 on the 7000 body and I tried it on the 810-FX body. I feel this lens is well balanced and its build solid. I have a bad habit when I put the camera on the table I set first on the lens than the camera body-with other lenses I have to be careful front lenses or zoom ring getting easily damaged.
Focusing I can’t say anything because the 7000 isn’t the strongest in it.
This lense does have lens distortion but it benefits me or better my model. And I got this lens used.
Something to laugh I got a silver 28-80mm 3.3-5.6 g fully plastic lens on my 810 body because I can’t find a lens what I like on my FX body
I