I don't believe such a device currently exists that you can mount on a bicycle, but there are devices that have characteristics similar to what you seek that you can mount a bicycle onto. They are specific types of bicycle trainers. The explanation is a bit long but if you understand how trainers work and how they compare to the work you do to move your bike outdoors on a real road you'll be better able to imagine what design challenges you'd face in creating the device you've imagined.

Outdoors on the road there are several sources of drag you must overcome. This bicycles.SE answer gives a fuller explanation but the short version is that there's a part of total drag that is constant with speed, a part that depends on your acceleration, a part that depends on climbing (or descending) a hill, and a part that depends on how aerodynamic you and your bike are. Importantly, the aerodynamic drag component doesn't scale linearly with your speed: it scales quadratically, so the the power needed to overcome aerodynamic drag varies with the cube of speed (assuming zero wind).

But the part that's related to your question is the "rolling resistance" component of drag. Rolling resistance is constant (that is, independent of speed) so the power needed to overcome rolling resistance is linear with speed. But the important part here is that the rolling resistance itself is constant. So if you are in a particular gear and you can ignore air resistance, your pedal load will be constant. If you speed up (and, since you're in a particular gear) your cadence will increase but the pedal load will be constant. This is the condition you were stating in your question.

Enter bicycle trainers. All bicycle trainers have a way to impose drag or to generate a load against which you pedal. You may be familiar with trainers that use turbines set into a fluid to create load, or wind trainers, or magnetic trainers. In general, the faster you pedal, the faster your rear wheel turns, which spins the trainer's load generator faster, which increases the load. Importantly, each trainer will have a different "load profile" which determines how its load increases with speed. Fluid and wind trainers (air can be considered a fluid) have the characteristic that their drag typically increases quadratically with wheel speed, like it does when you ride on a road outdoors. There are also bicycle trainers that act as ergometers; you set a particular target power and they adjust the load so that total power is maintained. If you pedal more slowly, the load increases to maintain targeted power load. If you pedal faster, the load decreases to maintain targeted power load. This is exactly opposite to what you want. However, there is a third type of training device: rollers. Typical rollers (that don't have any additional load generating device such as magnetic or fluid load units) have nearly constant drag -- which means that the power needed to overcome drag on rollers is nearly linear. So you're looking for a device that mimics rollers by adjusting the gear ratio to keep pedal loads constant.

What you seek is uncommon because most effort has been put into trying to make trainers less like rollers and more like riding on the road, where load increases nonlinearly. From an engineering point of view, it would be possible but from a marketing point of view, the demand works the other way.

I don't believe such a device currently exists that you can mount on a bicycle, but there are devices that have characteristics similar to what you seek that you can mount a bicycle onto. They are specific types of bicycle trainers. The explanation is a bit long but if you understand how trainers work and how they compare to the work you do to move your bike outdoors on a real road you'll be better able to imagine what design challenges you'd face in creating the device you've imagined.

Outdoors on the road there are several sources of drag you must overcome. This bicycles.SE answer gives a fuller explanation but the short version is that there's a part of total drag that is constant with speed, a part that depends on your acceleration, a part that depends on climbing (or descending) a hill, and a part that depends on how aerodynamic you and your bike are. Importantly, the aerodynamic drag component doesn't scale linearly with your speed: it scales quadratically, so the the power needed to overcome aerodynamic drag varies with the cube of speed (assuming zero wind).

But the part that's related to your question is the "rolling resistance" component of drag. Rolling resistance is constant (that is, independent of speed) so the power needed to overcome rolling resistance is linear with speed. But the important part here is that the rolling resistance itself is constant. So if you are in a particular gear and you can ignore air resistance, your pedal load will be constant. If you speed up (and, since you're in a particular gear) your cadence will increase but the pedal load will be constant. This is the condition you were stating in your question.

Enter bicycle trainers. All bicycle trainers have a way to impose drag or to generate a load against which you pedal. You may be familiar with trainers that use turbines set into a fluid to create load, or wind trainers, or magnetic trainers. In general, the faster you pedal, the faster your rear wheel turns, which spins the trainer's load generator faster, which increases the load. Importantly, each trainer will have a different "load profile" which determines how its load increases with speed. Fluid and wind trainers (air can be considered a fluid) have the characteristic that their drag typically increases quadratically with wheel speed, like it does when you ride on a road outdoors. There are also bicycle trainers that act as ergometers; you set a particular target power and they adjust the load so that total power is maintained. If you pedal more slowly, the load increases to maintain targeted power load. If you pedal faster, the load decreases to maintain targeted power load. This is exactly opposite to what you want. However, there is a third type of training device: rollers. Typical rollers (that don't have any additional load generating device such as magnetic or fluid load units) have nearly constant drag -- which means that the power needed to overcome drag on rollers is nearly linear. So you're looking for a device that mimics rollers by adjusting the gear ratio to keep pedal loads constant.

What you seek is uncommon because most effort has been put into trying to make trainers less like rollers and more like riding on the road, where load increases nonlinearly. From an engineering point of view, it would be possible but from a marketing point of view, the demand works the other way.