The thing is, this care helps kids with gender dysphoria to get through their teenage years and make it to adulthood. It can't simply be postponed until later without serious impact on the well being of the kid. We are talking about things like puberty blockers here, not surgeries:

Major medical associations agree that gender-affirming care is clinically appropriate for children and adults with gender dysphoria, which, according to the American Psychiatric Association, is psychological distress that may result when a person’s gender identity and sex assigned at birth do not align.

Though the care is highly individualized, some children may decide to use reversible puberty suppression therapy. This part of the process may also include hormone therapy that can lead to gender-affirming physical change. Surgical interventions, however, are not typically done on children and many health care providers do not offer them to minors. (CNN)

Gender dysphoria is by all accounts a deeply troubling experience during teenage years, particularly if your body is growing in a direction that makes you ever more uncomfortable. Puberty blockers can help:

For transgender and gender-diverse youth who have gender dysphoria, delaying puberty might:

• Improve mental well-being.
• Ease depression and anxiety.
• Improve social interactions with others.
• Lower the need for future surgeries.
• Ease thoughts or actions of self-harm. (Mayo Clinic)

You can't do this once you're already an adult, and there are physical changes you might be deeply uncomfortable with that can be locked in by puberty and will now require more radical interventions as an adult. I know trans adults who really struggle with the feeling that they should have started medical treatments sooner, before puberty brought changes to their bodies.

These treatments aren't prescribed lightly either, contrary to what some right-wing voices would have you imagine. From the same Mayo Clinic page:

In most cases, to begin using puberty blockers, an individual needs to:

• Show a lasting pattern of gender nonconformity or gender dysphoria.
• Have gender dysphoria that began or worsened at the start of puberty.
• Address any psychological, medical or social problems that could interfere with the treatment.
• Be able to understand the treatment and agree to have it. This is called informed consent.

Puberty blockers are not recommended for children who have not started puberty.