The smaller 'phone companies' don't typically operate their own RF network; they lease channels from the big players like Verizon, AT&T, and T-Mobile; and are referred to as as a 'virtual' phone companies'.
So, the good news is (ironically) that, as a Consumer Cellular customer, your calls are actually being handled by Verizon, AT&T, etc. But, the bad news is, your calls are typically allocated a lower priority when it comes to assigning channels; most apparent during times of high demand. The 'big boys' take care of their own, first!
Additionally, the employer owned phones of First Responders (typically in more urban situations) are assigned a higher priority ...... they will always be able to make a call regardless of how busy the network.
We're all equal ...... some are just more equal than others!