Unlike NiMH, NiCad, and lead-acid cells, Li-Ions are not pushed outside normal operating range when charging. For any other type of battery, that's not the case. A Li-Ion comes off the charger at the terminal voltage of the charger which is within the cells normal operating range.
There are two primary fault modes for a Li-Ion charger. It can either go over the cell's 4.2V operating limit (for a 3.7V nominal cell) or go over the cell's maximum tolerable current which depends on the size the cell itself. There are secondary safety points like cell temperature, but they generally are not monitored with an inexpensive charger.
If there's an issue with a Li-Ion charger on the market, it would be due to one of those two primary faults. Li-Ions do not become intolerant to their terminal voltage with wear. They simply lose capacity and don't run as long on a charge.
The main issue with using USB on larger cells is not due to the cells themselves, but the limits on current you see with USB ports. A USB charging port has a higher current limit so you can get around that issue when limited to that type of port. Another issue is the connector. The mini-B type connectors have lower current ratings than the regular A and B connectors. There's also the voltage drop across the cable itself. It can render a charger unable to charge a cell at its programmed rate.
There's another potential issue with high rates involving the charger itself. Heat can be a big problem. For example, if the you are using a 1A rate and the battery requires 3.5V at its current state of charge, there's a 1.5V difference between supply and output for the charger. Most USB chargers use a linear type of regulation so one would need to dissipate 1.5W for that example. That's quite a lot for a small chip. The charger controllers I use go into thermal regulation mode when they get too hot which drops down the charging rate quite a bit. Heat sinking is a major concern for those chips.