Online multiplayer has been around for quite some time now and has always been a great source of connectedness, especially for players with friends across vast distances. In many cases, it's actually the game that forges those connections between total strangers. Although for some time, the divisiveness of "console wars" had also led to the thinking that playing a game on a certain system would logically only limit them to playing with fellow players of the same game on the same system.
More and more multiplayer games are coming out with cross-play support to bridge the gap between players across different consoles. This means that players who are playing the same game can now play on the same servers as everyone -- regardless of the system they're playing the game on. This has raised concerns across the gaming community, especially on the topic of fairness. Some consoles are just better at some games than others - and it doesn't always have to do with the specs either. Differences in play style, available peripherals, and display screens can ultimately lead to different gameplay experiences. Someone who wants to enjoy a casual game of Fortnite on their Nintendo Switch, for example, might find themselves constantly bodied by other players on their PC gaming setups.
Cross-play is rendered ultimately pointless should a game that supports cross-play not have a cross-save function as well. Cross-save is when a player decides to migrate their game profile or data over from one platform to another, or the game servers themselves keeping the data updated on all platforms giving the players the chance to experience the game across different devices to best suit their playstyle - or even just whatever they feel like playing on. That said, most non-free games would probably have to be purchased multiple times -- a copy for each system.
Already most free-to-play games support cross-platform support or cross-play. Recent titles like Call of Duty: Warzone, Rogue Company, and Spellbreak have launched with cross-play from the start. Games like Fortnite tie player data into their Epic Games account provide cross-save support. Players can play on their PC or PlayStation and even enjoy the mobility options of playing on a Nintendo Switch or a smartphone with the same account, the same profile and the same achievements.
Some of the bigger games that allow for cross-play sorely lack a cross-save feature. Titles like Apex Legends or Mortal Kombat, while being popular across multiple consoles, have their adoring fanbase limited to whatever one system they have decided to invest their profile development into. Placing this decision in the player's hands ties them to just the one system they confine their accounts into. This should be fine should a game come out completely at the moment of your decision, but we all know that in this day and age, games are continuously evolving, with updates and changes and additional content coming out regularly. Such changes could sporadically affect which system might be deemed better for a player at any given time, which could lead to buyer's remorse. Of course there's always the option of starting everything from scratch again, but for some people, the time and effort put into developing their profiles are not worth recreating on another system. Worst case, they lose interest in the title altogether.
In the end, the means for both cross-play and cross-save is already there, as evidenced by what few titles are already providing support for both features. Other than title exclusivity, there really shouldn't be any reason for a game to not work on having both. The experience of playing the game on different systems, with different controls and on different displays.