1.) Bandwidth != latency, and jitter matters. A dedicated leased line's latency is constant and is generally substantially lower than a DSL or FIOS connection. This can be a critical point for certain types of applications. The upstream bandwidth from a given POP is certainly a point of variability, but generally far less so than consumer-oriented concentrators which can suffer in non-intuitive ways under periods of congestion.
2.) Consistency of bandwidth - If you lease a DS-3 then you have that bandwidth available at all times and under all circumstances. Even business-grade DSL/cable/similar services are subject to variations in available bandwidth based on usage. There's more bandwidth available under most conditions, but potentially less under others.
3.) Availability - At least in the US, traditional leased lines can be had anywhere. If your facility happens to be in an industrial park or located somewhat remotely then cable/DSL/FIOS may simply not be available at all. This is especially true in many commercial settings where a SONET mux may already be present but other services aren't economically viable for SP's.
4.) Mixture of services - Many SP's will offer Internet transit bandwidth as well as private WAN service on the same physical pipe. While this can be accomplished on a shared medium, better results are often had on dedicated pipes. Also, as antiquated as it may sound there is still a lot of use of standard PRI's rather than SIP trunks for a lot of phone systems. These can be mapped into a timeslot along with other services.
5.) To your first point, ALL Internet service is multiplexed. That's kind of the point. Without oversubscription networks don't really make a lot of sense. Predictability of the behavior of oversubscription is the point - and this isn't something that has been a major design goal of transports dedicated to consumer transport.
In practice I'd generally rather see a straight Ethernet connection run natively or mapped over a SONET circuit for sites with substantial bandwidth requirements but there are plenty of instances where traditional SONET framing is really the only practical solution. For edge sites the consumer edge services (inclusive of so-called business grade) are generally both sufficient and attractively priced.