Lowering the output of high amp current sensor for low amp use - good or bad?
As explained in Definition of amperage of non-invasive current transformer:

It may help to consider CTs as complimentary to VTs (voltage transformers).

Voltage transformers are quite happy with open circuits but dislike short circuits. There is a minimum value of resistance that can be applied as a load before the rating is exceeded.
Current transformers are very happy with a short-circuit load as it is very easy to maintain current. As the load resistance (called a &quot;burden&quot;) increases the voltage must increase to drive the current. At some point the VA rating will be exceeded. In the case of high-powered CTs an open-circuit can cause flashover as the voltage reaches kilovolts in an attempt to drive the current through.


Back to your question:
By increasing the value of burden resistor or turning the wire several times around the CT an output can be increased.
This is correct and is common practice. The CT has no idea of the number of primary turns so it just sees the total ampere-turns.
But is it a good practise to lower the high current non-invasive current sensor for low amp application in terms of harmonics, phase error and etc?
Wikipedia's Current transformer article says:

Phase shift
Ideally, the primary and secondary currents of a current transformer should be in phase. In practice, this is impossible, but, at normal power frequencies, phase shifts of a few tenths of a degree are achievable, while simpler CTs may have phase shifts up to six degrees.[2] For current measurement, phase shift is immaterial as ammeters only display the magnitude of the current. However, in wattmeters, energy meters, and power factor meters, phase shift produces errors. For power and energy measurement, the errors are considered to be negligible at unity power factor but become more significant as the power factor approaches zero. At zero power factor, all the measured power is due to the current transformer's phase error.[2] The introduction of electronic power and energy meters has allowed current phase error to be calibrated out.[3]

Increasing A-t is preferable to increasing the burden resistor.
Further reading:

Figure 1. Linearity of output voltage is controlled by using precision burden resistors and reducing the losses in the secondary coil of the transformer. This characteristic, along with the phase shift, are a measure of quality and design of a current transformer when used in the energy management industry. Source: OpenSourceMeter.com.

Current Transformers -
An Analysis of Ratio and Phase Angle Error by CR Magnetics.
Measurement errors due to phase shift.
This also seems to be a topic of interest at OpenEnergyMonitor.org. This site (rather than the forum) is worth a good look as they have tackled many of the problems with energy management and hardware and software are open source.