Is there a limit to how fast a machine can produce items, which would make using the later tier machines useless.

To make use of the later tiers, you really should combine this mod with a stacking mod, not only to save UPS but to also take full advantage of the speed.

If you didn't know, Technically a crafting machine is limited to one craft/cycle per tick. Using a stacking mod like (https://mods.factorio.com/mod/deadlock_stacked_recipes) allows you to get the full potential out of these faster machines.

Thank you for replying and for the idea of stacked recipes, I did not know about this mod

To answer your question: Yes there is.
Crafting (Along with many other things) are limited to one per tick. A "tick" is tied to the "Update" in "Update Per Second", otherwise known as UPS. So at a default UPS of 60, there's 60 ticks and thus 60 items per second.

Because Productivity bonus is a separate "craft" as you can also see in the progress bar inside of a crafting entity, this one is also limited to one per tick. You can have a maximum of 120 items being craft per entity per second this way, assuming enough Productivity %.

It is worth a warning that items being consumed that aren't part of a recipe (i.e. mining iron ores) do not abide by this limit, while the production will be. So if an entity, such as a miner, would create "600 items per second" (Without Productivity for simplicity's sake here), you would get 60 ores while your Iron patch would be drained out of 600 ores. The 540 excess ores that it drained would simply vanish into thin air.

This "tick rate limit" also exists for entities such as belts, which can carry a maximum of 60 items per second per side (so a maximum of 120 items per second if you have belts that are that fast). Last time I checked(0.17), Splitters also bug out when the speed exceeds 120/s with a filter; the filter will fail to function every now and then.