Date: 202101
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Weather elements / visibility: Fog
Aircraft: Light Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: SVFR
Mission: Passenger
Flight phase: Taxi
Airspace: Class C ZZZ
ATC / advisory: Tower ZZZ
Second aircraft: Commercial Fixed Wing
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Distraction; Situational Awareness; Communication Breakdown; Confusion
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: Taxi
Result: General None Reported / Taken
Contributing factors: Environment - Non Weather Related; Human Factors; ATC Equipment / Nav Facility / Buildings; Company Policy
Primary problem: Environment - Non Weather Related

Narrative: The event occurred because ZZZ is working a busy airport with one Controller utilizing all three frequencies. This is a major safety of flight issue as multiple links in the safety chain were broken that day. If the sharpness of the crews from Aircraft Y and Aircraft Z had not utilized full four ear policy and patience it could have been an issue. The actions taken by the ATC operation in ZZZ are uncalled for and unsafe. If this is overlooked there could be fatal consequences in the future. There are a few local airports in the area of ZZZ that are non-towered. If the Tower Controller delayed any further for us to be handed over to Departure; we could have had a collision or RA with an unknown aircraft all due to the unsafe actions of one Controller handling a workload bound for a minimum of two personal.On the morning of date; I was in command of flight Aircraft X; ZZZ to ZZZ1. The ZZZ Tower had one Controller working all three frequencies: clearance; ground; and Tower. This day was a busy morning with Aircraft A bound for ZZZ1; Aircraft Y to ZZZ3; Aircraft Z to ZZZ4; and us to ZZZ1 all departing at roughly the same time.When we called for our clearance on the delivery frequency; we noticed there was some bleed over as the Controller was issuing takeoff clearances. We had to repeat our request for a clearance but were given it with no issues.I released the brakes and we called for push shortly after. Aircraft Y also called for push after us. In the middle of our push back the Controller called on the ground frequency to inform Aircraft A of a delay to ZZZ2 for them.  The two began to have a conversation on ground of a game plan to be made. As their conversation occurred our Ramp crew disconnected the tow bar and gave the wave off for an all clear to a taxi.I noticed Aircraft Y had pushed off gate X and we were pushed off of X+1 with our nose in the direction of travel to only exit at [intersection] with a head on collision. First Officer and I finished our 'After Start Checklist' and cleared the area to begin our taxi. I switched on our taxi and nose lights to noticed Aircraft Y did the same. With the Controller and Aircraft A conversation occurring to what was now a clearance being given with a read back to follow there was no way for me or Aircraft Y to have confirmation one was waiting for the other.There was dense fog and low visibility on the ramp that morning. Tower does not control the ramp and a courtesy call is requested. The weather was so bad we had a takeoff alternate of ZZZ5 that morning.It was a frustrating situation as Aircraft Y and I could barely make out the 2nd half of each other's aircraft; so it was a game of chicken. I tried to call over the radio and speak over the clearance being given but it did not work.Ultimately; I turned off my lights to give Aircraft Y the right of way. As we began our taxi to Runway X Aircraft Z called clearance to get their clearance to ZZZ4 and that now was being broadcast over the ground frequency adding to the safety issue that no one moving on the aircraft surface could talk to each other.The Tower issued Aircraft Y their takeoff clearance and told us we were next. After we got our takeoff clearance; we began the takeoff roll with no issues. As we continued our takeoff climb Aircraft Z called the Controller over the ground frequency. All we heard was the Controller responding over the Tower frequency meaning he was working all three frequencies still. This delayed our hand-off to departure and made us uneasy as the Tower radar could not see our path beyond a certain mileage. As we checked in with ZZZ Departure we were given an instruction to contact ZZZ3 Center as our time had been too long and radar services with ZZZ could not be utilized further.This told me the ZZZ airport Controller took too long to hand us off and impeded the Departure Controller from doing their job properly. We did not have sufficient air traffic control separation all due to the unsafe practices of the ZZZ airport and Air Traffic Control operation at the airport of ZZZ.ZZZ needs to hire another Controller! There must be at least one person working Ground and Delivery while another separate Controller works Tower. The operation in ZZZ has been compromised and it is scary to think that the unsafe actions are acceptable to those working in the ATC system.




Synopsis: Air carrier Captain reported Air Traffic Controller was working Local; Ground; and Clearance Delivery on one frequency resulting in communication issues and a delayed hand-off to Departure Control.