Turning a old pc into a router (modem bottleneck?)

A modem is very simplistic compared to a router in its function. It main purpose is to be a media converter. It converts say signals that run over cable tv wire to ethernet. Most modems do not actually use a general purpose cpu to do this they have custom built chips that have been optimized to do just that one function. In general the modem will be able to run as fast as the service the ISP is offering in your area. Many of the newer cable modems are rated to run over 2gbit if a ISP would choose to offer the option.

The main thing slows the device home users call "routers" is the NAT function which is used to share 1 single public ip with multiple PC. The main limitation is that every packet must have the source ip and port numbers changed and all the header checksums recalculated. This is a CPU clock restriction not a memory restriction. It has a table of translated ports but this takes very little memory.

The better devices put out over the last few years they have moved this NAT function off the main cpu to custom chips. This means that the main cpu is not burdened by this so you see devices that can easily pass 1gbit between lan and wan.

The function you would use a actual PC for that would need memory and cpu is more a function of a firewall. It takes a lot more memory and cpu for example to actually inspect and filter data passing through. The other is VPN. Most smaller consumer routers will bottleneck the cpu trying to transfer say more than 30mbps of encrypted traffic. Now if you actually want to run a "router" that is running a routing protocol you also need more memory and cpu but this is not something a home user does.

So it depends what you need to do. In most cases the modem/routers that you buy capable of running as fast as the internet your ISP offers. Maybe if you are one of those lucky people that can get gigabit internet maybe there are concerns with some modems/routers but for the vast majority of people that just need to connect multiple devices to their internet connection the bottleneck is the ISP not the equipment.