How bad would it to be to allow partial house renovation in Agricola?
I think the house rule will be harmless, and also that after playing a few games, no one will take advantage of partial renovation - because it's a terrible idea. It also introduces unnecessary complexity.


Balance: The only balance consequence I see is that the Renovation action can be taken much more often than in standard Agricola. In principle, you could use this to deny the action to other players. In practice though, I doubt it would be worth it - there are plenty more valuable things to do than renovate, in most games.
Strategy: You simply do not have time to upgrade individual rooms. As you point out, that's expensive in reed, but critically, it's using an action each time. And what for? Renovating a single room to Clay gets you a measly one point. If you also require that subsequent rooms must be built of the more expensive material, and that the house doesn't count as Clay until all rooms are completed, then partial renovation is clearly a terrible idea.
Complexity: There is already a mechanism for handling surplus goods - purchasing of Improvements. The idea of Renovation is that it's a major action, that takes careful preparation and timing, and may or may not be a good idea, depending on your resources, whether you can buy a Major Improvement at the same time, and whether you need a better house for your Minors or Occupations. In gameplay terms, partial renovation serves no useful purpose.


The second rule, about building houses from arbitrary building resources, has the potential for greater impact, but again is complex. It makes it easier to build rooms, while removing the resource niche effect that players get by Renovating. For example, one reason to Renovate to clay might be to make use of clay resources, while everyone else fights it out for wood for their rooms. This house rule would remove that tactical possibility, which is a shame. This is important because rooms are required to have children, and your workers drive the economic engine of the game (this is the reason that cards like Wet Nurse are so powerful). So messing with the room mechanic is not a great idea.

Overall, I think this is a solution in search of a problem. Bear in mind that the many, many Occupations and Minor Improvements allow all sorts of interesting game adjustments, including building options and alternatives. For example the Conservator lets you Renovate to stone in a single action. My advice is to tell your players to deal with the rules as they are, get them more experienced, and move them on to the full game as quickly as possible. With 14 different cards to manage each game, they'll have more than enough to worry about without needing to take issue with odd questions of building realism.