During the interaction of intense femtosecond laser pulses with various targets, the natural mechanisms of laser energy transformation inherently lack temporal control and thus commonly do not provide opportunities for a controlled generation of a well-collimated, high-charge beam of ions with a given energy of particular interest. In an effort to alleviate this problem, it was recently proposed that the ions can be dragged by an electron bunch trapped in a controllably moving potential well formed by laser radiation. Such standing-wave acceleration (SWA) can be achieved through reflection of a chirped laser pulse from a mirror, which has been formulated as the concept of chirped-standing-wave acceleration (CSWA). Here we analyze general feasibility aspects of the SWA approach and demonstrate its reasonable robustness against field structure imperfections, such as those caused by misalignment, ellipticity and limited contrast. Using this we also identify prospects and limitations of the CSWA concept.