Does USB version speed matter for input devices?
If you don't notice a difference, it might not really matter. You can test your input delay by plugging in the mouse directly and measuring the polling rate, then measuring again through the hub.
Look for the download link that says "Direct Input mouse rate tool" here: https://blog.codinghorror.com/mouse-dpi-and-usb-polling-rate/
There are many tools that measure polling rate, here is a webpage that claims to do it. https://zowie.benq.com/ja/support/mouse-rate-checker.html
Most consumer mice are 125hz which is at most a 8ms delay. Gaming mice might go up to 1000hz which would be 1ms response time. I think at least USB 2.0 is required for 1000hz. 7ms is not much of a difference.
The actual time it takes for a signal to travel from the mouse through the hub and to the computer is likely less than 0.1ms. I think the most significant factor is the polling rate, or the hardware in the mouse. Some monitors have an input lag of more than 10ms. If you are gaming, a graphics card can take anywhere from 5ms to 100ms to display a frame, depending on things like vsync buffers and render time.
I expect the cost to be minimal. USB 1.1 was fairly widely popular, and wasn't considered slow for such devices. (It was just too slow for certain other types of devices.)
In many cases, all you need to worry about is the slowest link in the chain, also known as the bottleneck. It doesn't matter how fast other pieces of the communication can happen if there is one point which slows things down. If the mouse cursor feels instantly responsive and so the slowest point of the communication is the perception of the person interacting with technology that moves at the speed of computer circuitry, then there's no problem.
Keyboards really don't need tons of bandwidth. Even the few people who can type over 100 words per minute (like me) are probably only utilizing a bit more than 600 bytes per minute so any version of USB can handle that with ease. Gamepads that are similarly old will easily be satisfied with such old technology. (I'm not quite so sure about some of the newest gamepads, like ones that might also be compatible with modern video game consoles.) As for the mouse, you're likely fine but I could believe mouse movement might occasionally lag enough to be noticeable for some people. Certainly it would be within the realm of being quite tolerable for most people, but some people might be slightly annoyed.
The bigger impact may actually be how responsive other devices are, such as USB drives or networking devices that may benefit more from increased availability.
An example of where that isn't the case is 802.11, also known as wireless. If you have an 802.11ac device which is backwards compatible with 802.11n and 802.11g and 802.11b and perhaps 802.11a (the slowest of which is 802.11b), that 802.11b support actually really harms 802.11ac, even if it isn't being used much. The reason is that when the wireless access point does a routine 802.11b check, that requires that the equipment is unavailable for the amount of time it takes to communicate an 802.11b frame. And 802.11b frame takes a lot longer than an faster frame like an 802.11ac frame, so you could fit multiple 802.11ac communications in the time it takes for an 802.11b frame.
(That is a more extreme example. Similarly, and 802.11g frame would be faster than 802.11b but slower than 802.11n, and an 802.11n frame would be faster than 802.11g but slower than 802.11ac)
So, simply by plugging a USB 1.1 hub in, you might require more bandwidth/processing than some newer technology, using up more time with some motherboard resources. Perhaps the biggest impact would be upon other devices that could be using similar resources on the motherboard, and the most likely culprit may be other USB devices. It might place some circuitry into a slower-but-more-compatible mode, which might have side effects like slowing down transfer speed of a USB drive.
Related question: Why does Windows 10 assign different port numbers to the same USB port when plugging in 3.0 vs. 2.0 device? (grawity's answer shows that different USB controller circuitry gets involved for supporting older devices. In my opinion, what I think is likely is that using such older circuitry is not likely to be "more efficient because it distributes the load between multiple controllers". Rather, it is more likely that older communications standards will just slow things down overall, for reasons similar to the Wi-Fi example I described earlier.)
The additional delay from a USB hub is of order of tens of microseconds for low-speed hubs and under one microsecond for high speed hubs. Humans don't notice delays less than 100 milliseconds, and in fact many computer screens have a latency as long as 70 ms, which is about 1000 times longer.
So no, a 0.1% increase in total lag because of the USB hub will not matter in practice.