Can I reuse Httpclient in Integration tests in ASP.NET Core?

I have an Asp.net core 6 Web api.

I make Integration tests with xUnit following the pattern here. WebApplicationFactory creates a client which the tests can use to make calls to the application instance.

Now, xUnit runs the class constructor for every test. To share a member between all tests in a test class, you need to use a xUnit class fixture. This is the example from MSDN:

public class IndexPageTests : 
    IClassFixture<CustomWebApplicationFactory<RazorPagesProject.Startup>>
{
    private readonly HttpClient _client;
    private readonly CustomWebApplicationFactory<RazorPagesProject.Startup> 
        _factory;

    public IndexPageTests(
        CustomWebApplicationFactory<RazorPagesProject.Startup> factory)
    {
        _factory = factory;
        _client = factory.CreateClient(new WebApplicationFactoryClientOptions
            {
                AllowAutoRedirect = false
            });
    }

I don't understand - why they put the CreateClient method in the constructor? Obviously, it will create a new client for every test. Why don't we create a separate Fixture class, create the client there and just inject it in the Test class? For example:

public class TestFixture 
{
    public TestFixture()
    {
       var factory = new CustomWebApplicationFactory<RazorPagesProject.Startup>();
       Client = factory.CreateClient(new WebApplicationFactoryClientOptions
            {
                AllowAutoRedirect = false
            });
    }

    public HttpClient Client { get; }
}

public class TestClass : IClassFixture<TestFixture>
{
    private readonly TestFixture _fixture;

    public TestClass(TestFixture fixture)
    {
       _fixture = fixture;
    }


    [Fact]
    public async Task FirstTest()
    {
       // use the fixture client directly
       await _fixture.Client.GetAsync("..../url");
    }
}

Does anyone see a problem with this approach? Memory leaks or other issues? Is the fact that we instantiate CustomWebApplicationFactory<RazorPagesProject.Startup>() in the fixture constructor and not disposing it afterwards - causing memory problems, etc?