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Metasurfaces are subwavelength-thick constructs, consisting of discrete meta-atoms, providing discretized levels of phase accumulation that collectively approximate a designed optical functionality. The meta-atoms utilizing geometric phase with polarization-converting structures produced encouraging implementations of optical components including metalenses. However, to date, a pending and fundamental problem of this approach has been the low device efficiency that such resulting components suffer, an unwanted side effect of large lattice constants used for preventing inter-coupling of their meta-atoms. Although the use of near-field coupling for tuning electromagnetic resonances found its use in constructing efficient narrow-band designs, such structures fell short of providing high efficiency over a broad spectrum. Here, we propose and show that tightly packed fabric of identical dielectric nanopillar waveguides with continuously-tuned inter-coupling distances make excellent and complete achromatic metasurface elements. This architecture enables the scatterers to interact with the incoming wave extremely efficiently. As a proof-of-concept demonstration, we showed an achromatic cylindrical metalens, constructed from strongly coupled dielectric nanopillars of a single geometry as continuously-set phase elements in a 'meta-atomless' fashion, working in the entirety of 400-700 nm band. This metalens achieves over 85 percent focusing efficiency across this whole spectral range. To combat polarization sensitivity, we used hexagonally stacked nanopillars to build up a polarization-independent scatterer library. Finally, a circular metalens with polarization-independent operation and achromatic focusing was obtained. This is a paradigm shift in making an achromatic metasurface architecture by wovening identical nanopillars coupled into an irregular lattice constructed via careful tuning.