For anyone who stumbles across this, I solved it (webkit only firefox also seems to respect this) by making the calendar-picker-indicator
the full height and width of the input, as outlined here.
.input-container input {
border: none;
box-sizing: border-box;
outline: 0;
padding: .75rem;
position: relative;
width: 100%;
}
input[type="date"]::-webkit-calendar-picker-indicator {
background: transparent;
bottom: 0;
color: transparent;
cursor: pointer;
height: auto;
left: 0;
position: absolute;
right: 0;
top: 0;
width: auto;
}
<input type="date">