Recent denoising algorithms based on the "blind-spot" strategy show impressive blind image denoising performances, without utilizing any external dataset. While the methods excel in recovering highly contaminated images, we observe that such algorithms are often less effective under a low-noise or real noise regime. To address this gap, we propose an alternative denoising strategy that leverages the architectural inductive bias of implicit neural representations (INRs), based on our two findings: (1) INR tends to fit the low-frequency clean image signal faster than the high-frequency noise, and (2) INR layers that are closer to the output play more critical roles in fitting higher-frequency parts. Building on these observations, we propose a denoising algorithm that maximizes the innate denoising capability of INRs by penalizing the growth of deeper layer weights. We show that our method outperforms existing zero-shot denoising methods under an extensive set of low-noise or real-noise scenarios.