The CST-1020 looks to be similar to the CR3110 - a simple current transformer of about 1000:1 ratio. Whatever the AC current in the primary you get 1/1000 of that in the secondary. Another somewhat similar part is the CSE187L (used in the open energy monitor project).
The ACS712 has 1/2 Vcc at no current so it can run from a single supply and measure both polarities of current. It also makes connecting it to a single supply analog circuit like a microprocessor a/d converter easy. Claiming it was designed that way to overcome using a diode on the output is a stretch although it should work, especially with calibration. But if you want high accuracy you need to think about the variation of the diode voltage drop with temperature, etc.
Here's a link about current transformers and DC that google turned up:
https://www.crmagnetics.com/Products/Assets/ProductPDFs/Precision%20Rectifier%20Circuit%20for%20CT%20Signal%20Conditioning.pdf
The CR3110 circuit given earlier has the diodes before the load or "burden" resistor. The signal at this point is a current not a voltage to avoid the diode drop issue but as noted in the link the current transformer may not support the additional voltage. I think the CSE187L would be more likely to work given the conventional core but I don't know for sure. Make sure you don't use any current transformer without the load resistor - it will generate high voltages and could damage things.
The startup current on an induction motor can easily be more than twice it's rated running current. Before using the ACS712 solution I would want to check if it could handle over currents. High transient over currents shouldn't be an issue with the current transformers.
The ACS712 has 1/2 Vcc at no current so it can run from a single supply and measure both polarities of current. It also makes connecting it to a single supply analog circuit like a microprocessor a/d converter easy. Claiming it was designed that way to overcome using a diode on the output is a stretch although it should work, especially with calibration. But if you want high accuracy you need to think about the variation of the diode voltage drop with temperature, etc.
Here's a link about current transformers and DC that google turned up:
https://www.crmagnetics.com/Products/Assets/ProductPDFs/Precision%20Rectifier%20Circuit%20for%20CT%20Signal%20Conditioning.pdf
The CR3110 circuit given earlier has the diodes before the load or "burden" resistor. The signal at this point is a current not a voltage to avoid the diode drop issue but as noted in the link the current transformer may not support the additional voltage. I think the CSE187L would be more likely to work given the conventional core but I don't know for sure. Make sure you don't use any current transformer without the load resistor - it will generate high voltages and could damage things.
The startup current on an induction motor can easily be more than twice it's rated running current. Before using the ACS712 solution I would want to check if it could handle over currents. High transient over currents shouldn't be an issue with the current transformers.