If L1 is a problem, then L2 would be a problem as well. After all, at L2 the spacecraft is receiving its commands from the direction of the sun.
However, the problem is not quite as bad as it seems. Spacecraft at L1 and L2 Lagrange points actually are in a halo orbit that "orbits" around the Lagrange point. Attempting to stay at exactly the L1 or L2 point is unstable, since gravitational forces tend to knock you away from that point. The halo orbits are much more stable. And for a spacecraft in a halo orbit, you never have to point your antenna directly at the sun.
The problem is solvable for radio communication at least. There are currently 4 spacecraft orbiting the Earth-Sun L1 point (ACE, DSCOVR, SOHO, and WIND) as well as 3 spacecraft at the L2 point (Gaia, James Webb, and Spektr-RG).
However, the problem is not quite as bad as it seems. Spacecraft at L1 and L2 Lagrange points actually are in a halo orbit that "orbits" around the Lagrange point. Attempting to stay at exactly the L1 or L2 point is unstable, since gravitational forces tend to knock you away from that point. The halo orbits are much more stable. And for a spacecraft in a halo orbit, you never have to point your antenna directly at the sun.
The problem is solvable for radio communication at least. There are currently 4 spacecraft orbiting the Earth-Sun L1 point (ACE, DSCOVR, SOHO, and WIND) as well as 3 spacecraft at the L2 point (Gaia, James Webb, and Spektr-RG).