The policy was part of Labour's manifesto during the general election last year and was implemented on 1 January across the UK.
Sir James Eadie, the First Treasury Counsel, told the court there was no obligation for the government to subsidise private education in any way.
The main objective of the VAT policy is to raise additional tax revenue to invest in public services, "including the state education system", the government argued.
It consulted extensively on the policy design, "weighing the pros and cons" of possible exemptions for small faith schools, international schools and children with special education needs.
They also looked at whether introducing it in September 2025, rather than January 2025, would be more appropriate, the court was told.
The government said it rejected the exemptions after a consultation, arguing it would be "unworkable and administratively onerous" and that delaying the timing of it coming in would affect the amount of money it raised.
Only fees for children with a local authority education, health and care plan (EHCP) which names their specific school will continue to be exempt.
Sir James said parents who wish to opt out of the system of "universally accessible, state-funded education" are free to choose any private education for their child that they can afford, or "to educate their child at home".
The argument that increasing the cost to parents who choose a private school would be an infringement of the common law "is plainly not right", he wrote in his submissions.
The government wants all three claims to be dismissed.