Making an obstruction avoiding device without microcontroller
No, this won't really work.  Your idea sortof makes sense in theory, but you are missing some down to earth practicality issues.

First, consider the kind of currents the motors in even a small toy would require.  Then consider how low a resistance the LDR would need to have so that the voltage drop to the right motor is negligible.  It would probably need to be less than 1 &Omega;, which is well below the practical range for LDRs.

Even if this did work, it would not be very efficient and the LDR would dissipate significant power when it is in the half-on state.  Wasting power is not a good thing when batteries are in use.  LDRs are much more suitalble as sensors instead of resistive pass elements for significant power.

You have given no valid reason for avoiding a microcontroller, probably because there is none.  If your reasons are religious, then your whole question is off topic here.  This is a engineering site where we discuss solutions to real problems.

A microcontroller reading light intensity from a LDR used as sensor, then driving each motor with PWM to modulate its drive level is the obvious and efficient way of doing this.  With that setup, it would be simple to have two LDRs, one on each side, and have the device always drive towards the strongest light.

Added:

I see in some comments you made (now deleted) that you think avoiding a microcontroller reduces cost.  This is not true.  Using a microcontroller will be the lowest cost solution that actually works.  You mentioned the price of a arduino, but only a tiny fraction of that is the cost of the microcontroller, so is not relevant.  The motors, mechanical drive train assembly, and battery will all cost more than a reasonable microcontroller for this job.  Many micros are available for under $1.  I didn't look all that carefully, but from a first glance a PIC 12F1501 looks like it can do this job.  It is listed as $.49 in 5k quantity.

Added 2:

Since there is some objection to providing only the 5k quantity price here for some reason, I looked up a example version of this part on microchipdirect, just like anyone else can do that wants detailed pricing.  You could also look on distributor web sites, like Mouser.  There are lots of places to buy PICs in various quantities.

Specifically, as a example, the PIC 12F1501-I/SN, which is the commerical temperature grade in SOIC package is available on microchipdirect in single pieces with the price for up to 25 units being $.67 each.  Of course there is shipping added to that, so buying a single unit is silly.  Generally you'd buy a bunch of parts for a whole project at once, preferably with a few spares from Mouser or wherever.  All I'm trying to point out is that these things are cheap and to give a rough idea of price.  The details are the job of anyone actually doing the design to chase down, as always.