Since you have an old car battery, the cost of damaging it by overcharging isn't much ($40?) and that would only happen if it got a lot of sun over weeks. A small home solar system might have thousands of dollars of batteries, so standard practice has long been for those to always have charge controllers.
For small systems the cost of a charge controller used to be significant so it was common to forego it in favor of simplicity. However, there are now very - inexpensive - controllers which no longer as easily justify the old practice.
If you can afford an additional $25, you might as well do it right. Also, it would come with instructions on what to do.
When dealing in watts and watt-hours, it helps to get your math right if you compute a single unit's capacity, then simply multiply by the number of units. E.G. Go 115AH x 12 (not 24) volts to get 1380 watt-hours per battery, then multiply by the number of batteries, 1380WH x 4 = 5520WH whole pack.
I have no idea where you got 54V for 6 ra-220 panels in series (not parallel). You seem to be assuming 9V per panel, at 30A, = 270 watts per panel. See how much nicer "per unit" works? It's now obvious something is wrong with the math, since these panels are only rated at 220-230W. 225W x 6 = 1350W, but that's perfect conditions.
For general design, focus on the watts. The MPPT controller will sort out the volts and amps. However, you do need to make sure the "open circuit" voltage of the panels is appropriate for the MPPT controller.
Also, don't plan to bottom out the batteries if you're buying lead-acid. They are happiest when they never drop below 70% charge (i.e. only using the top 30% of charge in the battery). Dropping below 50% should be uncommon, and draining dead should be rare. Doing so prematurely ages the battery.
If you want a battery you can frequently deep discharge and otherwise abuse, look at Nickel-Iron or Nickel-Cadmium (not NiMH).
Best Answer
Those MPPT controllers seem appropriately sized compared to panel capacity. The panels might output slightly more under absolutely ideal conditions, but those are rare.
70A into a 450 amp-hour battery means you would recharge them from zero in 6.5 hours (which you should not ever do, allowing lead-acids to fall anywhere near zero, that is).
So your charging rate is 0.1555 "C", which is high, but still within limits for lead-acid. It may tend to heat up a bit given the fairly fast recharge rate, which may cause high water use. Be careful; use distilled water for makeup water, because if you're frequently adding water, that means any impurities in the water get concentrated fast.