In fact, regeneration is applied by God's Spirit prior to the offer of salvation. That grace makes the individual able and willing to believe or accept the offer. Romans teaches that by nature no one seeketh after God. By nature, no one wants to be saved. Hence, no one can accept the offer of salvation unless they are regenerated and made willing to accept the offer. A salvation that can be accepted or rejected by a sinner is a salvation that is earned. This is so because it is predicated on the autonomous ability to accept the offer. Grace that is earned thereby is not grace.
A dollar bill that is rejected is still a dollar bill bill. But grace that is earned is not grace. If there was something in the person that gave them the power to accept the offer, then salvation would be predicated on the inherent ability to accept that offer. Salvation would be based on something meritorious in the individual. Hence, the gift would no longer be of grace.
You raise a curious and clever argument. Unfortunately, you are slipping dangerously into pelagianism. Be careful my friend.
Your post assumes the philosophical argument that guides calvinism and then uses it to justify irresistible grace.
The above post presents the bible information on times when grace has been resisted and then builds a doctrine.