In Tal Afar, I started out with a completely mechanized heavy unit - 8 tanks and 8 Bradleys. Later, we got some HMMWVs and some additional M113s. This gave us a great deal of flexibility. We would execute patrols with different vehicle sets for different missions.
For instance, tanks (and Bradleys) could conduct 2-vehicle patrols and longer-range night observation missions. We often had to commit a tank section to overwatch a key highway. The tanks could use their long-range thermal sights to see quite a ways. It was critical for the crew to position themselves to take advantage of this, as well as pull good security.
Also, we conducted lots of 2-tank patrols to keep the enemy off-balance and deny them freedom to 'maneuver' (plant very large IEDs). Some of these were the dreaded 'presence' patrol, but their presence kept the enemy at home and ensured OUR freedom of maneuver. Often, a tank section would patrol while an infantry squad conducted a dismounted patrol. The tank created noise that allowed the infantry squad to get into its observation or ambush position while also providing some very responsive heavy QRF capability.
For joint patrols with the Iraqi Army, we did things differently. Obviously the infantry platoons were well set up for this - ride to the Iraqi Army outpost, dismount, linkup, and conduct a joint patrol. They had the manpower to provide overwatch from bounding fire teams. For a tank platoon, what worked best was a single M113 and 2 tanks. Two crews would ride the M113 to the IA outpost, dismount, and conduct a patrol, with the M113 following the patrol. This put six or seven Soldiers on the ground with the IA. The M113 provided ECM coverage, a single heavy machine gun, long-range radio, and CASEVAC. The tanks would provide some overwatch or patrol an adjacent street. The IA liked this more than what 3ACR had done, with tankers on tanks and the IA on the ground (of course the fight had evolved - 3ACR had been in big fights and the tankers were used to shooting from their vehicle). You share some risk, you gain some respect. And they didn't mind the firepower at all...
As we fielded uparmored HMMWVs, we used them more and more. However, for executing larger dismounted missions, they were not very effective as you don't get a lot of dismounts per vehicle. Instead, we would revert back to our M113s again. 3 M113s (manned by mechanics) with tankers inside was a valid package to execute a small raid.
When we got to Ramadi, though, I had a platoon that went right back to tanks and fired a large amount of rounds in direct support of a Marine infantry battalion. Another platoon used a section of tanks regularly for night overwatch. The third platoon used a section of tanks once in five months. My HQ, run by myself or my XO, would conduct a night overwatch mission every few days on the highway, watching for IED emplacers, using the tank thermal sights. In our last few days in Tal Afar, we had rarely used tanks, yet as soon as we hit a new AO, they became very popular again.
Flexibility in being comfortable/competent in multiple vehicle platforms was a key characteristic of mech forces. There was just too much ground to cover to walk everywhere. However, you do have to balance this against increased logistical requirements and fewer dismounts available. But then, these problems have existed since we had horses in the Army.
Dr. Nathan Toronto and I published a response to Lyall and Wilson in Routledge's "Small Wars and Insurgencies". Unfotunately it isn't publically available and costs a lot, but nearly all our points/arguments are listed above as to why their thesis is fundamentally flawed.
A mix is nice...
"A Sherman can give you a very nice... edge."- Oddball, 
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