If you use a comparator with a dispenser, you can fire continuously what is inside the dispenser.
When you attach a hopper to a dispenser, it put inside the dispenser any item available (throwed at the hopper or from a chest).

Sadly you can't do both together : having a dispenser continuously shooting and continuously filled by a hopper. This come from teh fact taht the hopper propagate redstone signal to the hopper and so stop itself.

What I expected to happen was...:
Having the dispenser firing anything I put inside the connected hopper

What actually happened was...:
The hopper stopped grabbing items as soon as the dispenser is powered

Steps to Reproduce:
1. put a dispenser and a dropper attached to it
2. power the dispenser (any ways)
3. try to put things inside the hopper and see that they are not grabbed by the dispenser as soon as the dispenser is powered

Picture 1 : comparator+dispenser -> continuously shooting arrows I put manually
Picture 2 : comparator+dispenser+hopper -> the hopper doesn't grab items
Picture 3 : dispenser+hopper -> the hopper grabbed some arrows because the dispenser was unpowered
Picture 4 : repowering will launch teh arrows but prevent the hopper to work again

Using a clock is solving this but will need more space and might be quite painful as the design here is rather simple (but doesn't work, sadly).

The fact that redstone signal go through dispenser is it really useful ? Glass block don't propagate redstone signal.

Hoping : Having an answer other than just "build a clock".