The MAC sublayer does what the PHY layer should be doing: detection (error, collision), channel listening, analog-to-digital and digital-to-analog translation, etc.
No. The physical layer moves bits from one end of a cable to the other end. Channel arbitration (together with MAC), line code, analog stuff etc is all physical layer.
What differs the LLC sublayer from the MAC sublayer?
The MAC sublayer belongs to the data link layer. Its main purpose is framing and to direct those data frames across a network using some kind of addressing (many protocols use MAC addresses). Commonly, the MAC sublayer also handles error detection.
The LLC sublayer sits on top of the MAC layer within the data link layer. Its main purpose is to multiplex the protocols that may concurrently use the MAC layer (like IPv4, IPv6, IPX, Ethertalk, ...). It may also be used to retransmit error frames detected by MAC.
Mulitplexing the data link layer (L2) means that multiple upper-layer protocols can share the same network - especially network layer ones like IPv4, IPv6, IPX, but also other protocols using L2 like xSTP, LLDP, FCoE, PPoE, etc).
That sharing works on a frame-to-frame basis by indicating each frame's payload association. On plain Ethernet, usually just the EtherType field does that job but other L2 protocols or variants require a distinct LLC sublayer.