Why is balancing used for lithium batteries only?

The answers provided so far are a little light on the actual mechanics that warrant balancing on Lithium chemistries and not on others.

First of all; all battery chemistries benefit greatly from proper balancing. Balancers are used on spacecraft nickel cadmium batteries, certain types of (low discharge) lead acid batteries and so on. All battery chemistries are just a certain dominant chemical reduction-oxidation reaction which occurs between certain Gibbs energies (or Redox potentials if you take into account both the anode and cathode reactions) - hence between a certain lower and higher voltage level. Above or below this 'ideal' range of voltages, other reactions may occur - or otherwise minority reactions become dominant.

These other reactions often are not reversible, hence they reduce the amount of 'useful' anode and cathode material, reducing capacity. Sometimes such unwanted reactions are even more dramatic, creating compounds that corrode the electrodes, degrade the electrolyte or cause toxic/explosive chemicals to form.

Now, these dangerous reactions are the primary reason why lithium chemistries really require safety circuits. Both when overcharging and overdischarging, depending on the electrolyte used, an explosive gas mixture is formed. More importantly, when the anode becomes too hot (about 125C), an exothermic reaction starts which accelerates itself, consuming most of the energy stored in the battery (thermal runaway). This is often caused by self-heating when dealing with large discharge currents, or with unwanted reactions caused by overcharging. As lithium chemistry batteries have energy densities up to more than an order of magnitude more than nickel and lead chemistries, i.e. a lot of energy in a small place, this can cause a big boom. Especially when combined with an explosive hydrogen-oxygen atmosphere.

Other chemistries have the same problem, though! Wet-cell Lead acid batteries are very well-known for producing hydrogen gas, even in 'normal' use, but mostly when abusing the cells. Lead acid cells can also go into thermal runaway when the sulphuric acid is concentrated enough. However, because of the relatively low energy density and high thermal capacity of the plates, as well as the high temperature at which thermal runaway kicks in compared to lithium ion, this is not a risk that needs to be dealt with in most situations. And the same goes for nickel chemistries, which often come with balancers in high-current applications (e.g. RC cars) - or your battery will only last 10-50 charges.

Then there's the practical question: can you just put lots of cells in series and pretend it's one big high voltage cell? Yes, you can, but the battery lifetime will be horrible. Any cell mismatch in your 12-cell stack will be exacerbated each charge-discharge cycle, and after a couple tens or maybe 100 charge cycles you will have a dead battery. It may even cause a safety hazard. So both for your safety and optimal use of the batteries it is very strongly recommended to use balanced charge management.

Lead acid batteries are OK with a certain float charge current forever. Lithium batteries would be damaged that way. When a lithium battery is full, trying to charge it more will cause damage. Conversely, in a car the "12 V" lead-acid battery is usually just charged with a fixed voltage of about 13.6 V. At that voltage it will take a small amount of charge current even when full, but unlike with a lithium battery, this does the lead-acid battery no harm.

Cells vary from battery to battery more than multi-cell mismatch in same construction. Hence 6 cell lead acid are treated as one. Since aging and capacity of unit is accelerated by weakest cell being depleted first, it is more critical with Lithium to optimize matching to improve overall capacity and prevent overcharging of weakest cell. Active zener clamp on each cell is needed to prevent overcharge.

However lead acid batteries will fail on 1 cell first more often than all degrade the same, but cost effectiveness does not warrant this added cost to extend life.

Also since self-heating accelerates aging in Lithium, they prefer fast charge and cutoff rather than rapid charge and CV charge of 14.2 of lead acid for float. SLA's are similar but lower voltage that is also temp compensated.