It appears to me that Part 97 requires the station to ID with the call sign of the licensee - not that of the remote control operator. That would preclude any remote operator from winning any contests under his own personal call sign.
There are some exceptions. The bolded parts are the key to this answer..
§ 97.109 Station control.(a) Each amateur station must have at least one control point.
(b) When a station is being locally controlled, the control operator must be at the control point. Any station may be locally controlled.
(c) When a station is being remotely controlled, the control operator must be at the control point. Any station may be remotely controlled.§ 97.103 Station licensee responsibilities.(a) The station licensee is responsible for the proper operation of the station in accordance with the FCC Rules. When the control operator is a different amateur operator than the station licensee, both persons are equally responsible for proper operation of the station.
(b) The station licensee must designate the station control operator. The FCC will presume that the station licensee is also the control operator, unless documentation to the contrary is in the station records.(c) The station licensee must make the station and the station records available for inspection upon request by an FCC representative.
§ 97.105 Control operator duties.(a) The control operator must ensure the immediate proper operation of the station, regardless of the type of control.(b) A station may only be operated in the manner and to the extent permitted by the privileges authorized for the class of operator license held by the control operator.
§ 97.5 Station license required.(
a) The station apparatus must be under the physical control of a person named in an amateur station license grant on the ULS consolidated license database or a person authorized for alien reciprocal operation by § 97.107 of this part, before the station may transmit on any amateur service frequency from any place that is:
(1) Within 50 km of the Earth's surface and at a place where the amateur service is regulated by the FCC;§ 97.119 Station identification.(a) Each amateur station, except a space station or telecommand station, must transmit its assigned call sign on its transmitting channel at the end of each communication, and at least every 10 minutes during a communication, for the purpose of clearly making the source of the transmissions from the station known to those receiving the transmissions. No station may transmit unidentified communications or signals, or transmit as the station call sign, any call sign not authorized to the station.Here is the relevant rule that brings this all together:
§ 97.213 Telecommand of an amateur station.An amateur station on or within 50 km of the Earth's surface may be under telecommand where:
(a) There is a radio or wireline control link between the control point and the station sufficient for the control operator to perform his/her duties. If radio, the control link must use an auxiliary station. A control link using a fiber optic cable or another telecommunication service is considered wireline.
(b) Provisions are incorporated to limit transmission by the station to a period of no more than 3 minutes in the event of malfunction in the control link.
(c) The station is protected against making, willfully or negligently, unauthorized transmissions.
(d) A photocopy of the station license and a label with the name, address, and telephone number of the station licensee and at least one designated control operator is posted in a conspicuous place at the station location.§ 97.3 Definitions.(a) The definitions of terms used in part 97 are:
(13) Control operator. An amateur operator designated by the licensee of a station to be responsible for the transmissions from that station to assure compliance with the FCC Rules.
(14) Control point. The location at which the control operator function is performed.
(44) Telecommand. A one-way transmission to initiate, modify, or terminate functions of a device at a distance.My interpretation is that a pile of equipment may be operated by a duly licensed amateur, within the privileges of the license, as long as the documentation exists that assigns that licensee as the control operator. No different than if you were to rent a handie talkie for use at some event or camping trip. As long as you have wireline control, and there is a transmit time limiter that can sense loss of control and shut down the transmitter within 3 minutes of loss of control.
This may presume that the entire Internet link is over terrestrial wire or fiber links. Since this would be very difficult to verify for the consumer of such, there does exist the simple system that is used by commercial radio stations all across the land... Telephone remote control. This could be a commercial type transmitter remote control, or a homebrew analog phone with a relay attached to the ringer that would trigger a radio to standby. It just needs to work.
There are probably some scenarios implementing a mixture of V/U repeaters, a radio link system, or 10m repeater link to serve as an "auxiliary station" that might comply with the intent of the rules.
If an owner of a pile of equipment posts documentation designating the current lessee of the pile of equipment as the control operator, and the pile of equipment can be controlled over the internet, and also dialed up on the phone and shut down, then this would be perfectly within Part 97 rules. The control operator uses his own callsign, stays within his license privileges, and all is good. When the lease is up, the control operator documentation is removed, and the station reverts to being a pile of equipment waiting for the next lessee.
Ideally, but not exclusively, this sort of system would be under the guidance of a duly FCC licensed amateur radio operator who could also go through the formality of transferring control operation to and from lessees, and performing routine station maintenance.