Led Zeppelin was impressive for many reasons, including the fact that they relied on musicianship and live performance to produce live arrangements of heavily produced and overdubbed songs that everyone knows. They did not use extra players, recorded tracks, or excessive harmonizers to do more than four players could do with their own four mouths, eight hands, and eight feet.
Their main live setup was like pre-Hagar Van Halen: singer, guitar, bass and drums. Without all the overdubs used in the studio, this left a lot of gaps in the sound spectrum. And the chords went away during solos. Their old school way to fill these gaps included a prominent bass guitar, busier drums, busier vocals, busier guitar playing, more distortion (i.e. harmonic content) on guitar, dense reverbs and one of their trademark live tools, the tape echo. Their other main setup was for John Paul Jones to play keyboard with his right hand and keyboard bass with his left hand. On Stairway to Heaven, he covered the flute parts with the Mellotron, but then switched to Fender Rhodes electric piano, and Fender Rhodes keyboard bass. This approach was how the Doors performed: singer, guitar, drums and double-duty keyboardist. With this approach, the chords don't go away during the guitar solo.
So yes, you can do without the chords during solos. This is more successful in some songs than others, and smart arrangements can make a big difference. One of the best stand-alone bass lines that comes to mind is in Stupid Girl. When I play in a Zeppelin-like line-up, I look for ways to augment the bass parts with more chords and busier accompaniments. Support players or backing tracks are a matter of personal choice - yes, it helps, but some people feel like the fun of a challenge and/or the musical integrity are lost. To me, harmonizers (they add notes to an instrument, such as adding corresponding guitar chords to bass guitar notes) are just a different version of the same thing: technology performs miracles that the bass player cannot. The only difference is that the extra notes are generated in real time, rather than recorded in advance. Again, it's personal choice.
The problem with a harmonizer is that it does not sound exactly right. The notes track the bass more precisely than a real guitar, so even if the sound replication is perfect (and I haven't heard one that is), the lack of interaction between the two sounds would still give it an artificial sound.
If you absolutely refuse to enlist help or use tracks or harmonizers, the only way to preserve the accompanying chords is to use the keyboards instead of the bass guitar. Although some Hammond organ players have gotten away with using just one instrument to cover bass and keys, it's generally best to use separate sounds for bass and the chords. You can either use two keyboards, or you can split a single keyboard, playing bass parts in the bass clef range and chords in the treble clef range. I have found this approach most successful when the different sounds are treated separately, in different mixer channels or different amplifiers.