There have been several crashes due to ice on wings destroying lift. One of the issues with this is that you can't detect that you don't have sufficient lift until you're already in the air, way too late to abort. Some aircraft have weighing scales in the landing gear. Could these be used to verify the expected lift, and abort if an anomaly was detected before $V_1$?
Technically one could develop a system that compares the decrease in weight-on-wheels during the take-off run to a theoretical lift model in order to determine whether the wings are performing as expected.
I see a number of reasons why this will not be successful a product:
Limited benefits: The benefit of such a system is minimal. There are very few crashes due to contaminated wings or wrong flap/slat configurations. Let's assume there are one hundred thousand airline flights per day and one lift related take-off crash every 4 years. That is one in 150 million.
Available alternatives. For both causes there are viable alternatives to detect them well before V1. Visual inspection of the wing usually detects contamination and many aircraft automatically check for the take-off configuration to be set whenever the thrust increases beyond a pre-defined trigger level.
Increase in number of rejected take-offs: No system is perfect. It will detect some contaminated wing situations and save the day, but it will also cry wolf in cases where there is nothing to abort a take-off for. If the system has a false alert rate of one in ten thousand take-offs (which would be very good and expensive to design and certify) it would cause 15000 aborted take-offs (assuming the same numbers as above) for every crash it prevents (assuming a missed alert rate of 0).
Since lift increases with the square of air speed, it is difficult to detect lack of lift early on during the take-off run. At low speed there is relatively little lift to be expected and it will be in the noise of the measurement. Also the accuracy of the airspeed indicator is relatively low at low speeds, so the theoretical lift model will not give accurate results either. As a consequence the system will only be able to detect lack of lift at high speeds. At those higher speeds, the influence of bumps in the runway start to affect the measurements as well. It is easy to see that detecting lack of lift is no so straight forward. False alerts will be raised and they will be at raised at high speeds.
High speed rejected take-offs are risky.
Boeing studies indicate that approximately 75 percent of RTOs are initiated at speeds less than 80 kt and rarely result in an accident. About 2 percent occur at speeds in excess of 120 kt. The overruns and incidents that occur invariably stem from these high-speed events.
So effectively such a system will likely increase the number of accidents.
Icing primarily occurs in the air. Icing does not normally occur on the ground, except during conditions of freezing rain, which obviously the crew will be aware of because they must positively acknowledge weather conditions before getting a taxi clearance.
An aircraft will normally never take off if there is anything on the wings. The wings have to be absolutely clean before a pilot sets in motion a flight. Operating an aircraft with anything non-approved on the wing is a complete violation of FAA regulations and highly dangerous.
Apparently in some instances pilots have taken off even though conditions of freezing rain have loaded down a wing with ice--sometimes with fatal results. Obviously such actions are reckless in the extreme and indicate the crew has not only not done a walkaround or checklist, but not even bothered to look at the wing. As a pilot, I would consider doing something like this unthinkable, but apparently there are some pilots who have done this.
Although your idea of using wheel strut scales to avoid this is interesting and innovative, it may be difficult to put it into practice because the weight of the ice will be relatively small compared to the overall weight of the aircraft. Also, if the pilots are so reckless as to not visually check their wings during a freezing rain storm, doing spreadsheet-like calculations to trying to detect ice by weight are certainly not going to be on their agenda.