How would the price of Bitcoin change if there were no other cryptocurrency than Bitcoin?
You can sum the whole cryptocurrency market capitalization, and calculate the prize of a single Bitcoin, based on that. But of course, the final result could be higher or lower than today's price, because then, the whole history of Bitcoin development could be different.
Would Bitcoin develop faster without a competition?
There will always be some competition. For example, fiat currencies could still exist in such scenario. But of course, in that case, it would be harder to create any new currency (crypto or not), and have it fully disconnected with Bitcoin. Because it will be extremely easy to create a peg between any coin you want.
But, in my opinion, the price of Bitcoin is lower if it does not have a competition. Why? Because if there is no competition, the buyer's thinking is "should I buy this or not?" however if there is competition, the buyer's mind is "should I buy Bitcoin or these alts?"
The question could be different than you can think of. It could be, for example: "Should I buy Bitcoin, and activate feature X on my coins or not?". If there are no altcoins, it means there was no reason to create them. Which means, you would have decentralized development, and (consequently) you could pick any feature X, and have it enabled or disabled specifically on the coins you own.
For example, one of the first altcoins, was NameCoin. Which means, if BitDNS or NameCoin would exist only on Bitcoin, then you would have that question: "Do you want to enable processing domain names in your fully decentralized node?". And also: "Do you want to register a name XYZ with your ABC coins, by making a signature, and broadcasting it to NameCoin?". All coins could have full two-way-peg. Which means, you could tell the world: "here is my 1 BTC". And if some nodes would enable "decentralized names", then that nodes would also know: "Hey, that address registered a name XYZ!". But it would be fully optional, and you would just pick features you want to have, and turn them on and off, without any restrictions, according to the rules of each optional subnetwork (note that "subnetwork" in that context would mean "a group of Bitcoin nodes, with activated feature X on relay-level").
NameCoin or BitDNS is easy, because it can work fine on signature-level-only. You don't have to move any coins at all, you can just say "name X is attached to coin Y, as long as coin Y is not moved", and it will be fine (also, in this case, you can decide with each on-chain transaction, if you want to keep that name, or release it). And if you want to pay for domain registration, then you can do that in your transaction fee, and attach a commitment, to any address type you want (it works even on P2PK), and kill two birds with one stone: send some payment, and register a new name, within a single transaction, that would take the same on-chain size, even if you won't register any new name at all. Also, it would be possible, to re-assign your name, without touching your coins, because "the network of decentralized naming nodes" would dictate their "name-based consensus", that could be fully independent from "coin-based consensus" if needed.
Going further, there would be no "new-mining-algo-based altcoins", just to make mining easier. People could stay on SHA-256, and focus fully on that, and just receive a different amount of coins in a fully decentralized way (and also mine Bitcoin at the same time, because Satoshi invented Merged Mining). However, if there would be any need to use a different hash function, then still, it is possible to do so, without creating any new altcoin. It is possible to create a market, where some people would sell their SHA-3-based shares to some Bitcoiners. It is the same case as with selling names in NameCoin or BitDNS. The product is different, but the marketplace could be done in the same way. And it is possible to create some P2P-based marketplace. Even Satoshi wanted to do so, when he created market.h and market.cpp files in the source code, but then he removed it, and nobody brought it back since then.
By the way, the main reason to switch into Scrypt or other hash functions, was because altcoins were attacked, when they didn't implement Merged Mining properly. Which means, if no altcoins would ever be created, they would use Merged Mining (or any other protection) from the very beginning, so there could be no need to ever switch from SHA-256 to anything else. Everything could be handled by commitments, and consequently, any new feature would require no additional Genesis Block at all. New features would be just enabled from block number N, and some miner could just include a commitment into any regular transaction, and activate any feature since then, or even leave it activated as "always was possible", and then the Genesis Block (of a feature X) would always point at 3rd January, 2009.
Another interesting consequence is that some people would like to change the amount of coins in circulation. For example, Litecoin made 4x increase. If there would be no altcoins, then there would be no need to do so. But assuming that some people would want it anyway, the whole thing could be achieved just by going below a single satoshi. Which means, it could be possible to own 0.25 satoshi in a Litecoin commitment network. It could be expressed on-chain, for example by 4-of-4 multisig, where a single satoshi could require four signatures, and each individual would own 0.25 satoshi separately. Of course, on-chain fees would still apply, which means, going below a single satoshi could be not worth it at times, where the standard fee was 0.01 BTC.
Of course, there are more altcoins and features to discuss, including Monero, Pedersen Commitments, cut-through, different elliptic curves, Turing-complete Script on Bitcoin, and so on. But I hope those paragraphs above are a good start to raise more questions. And also remember, that all of it is just "what if", and the "if" condition is already false, because altcoins are already there. But well, what stops us, humans, from dreaming?
As a result, not just Bitcoin but other altcoins will benefit. So, rather than being upset or sad because there is a competition, we can look at it in a positive way.
I am rather "upset or sad", because I can imagine, what could happen, when sidechains could be active. Especially no-fork sidechains, where you could just release a new client, without asking anyone, and have a fully-working two-way-peg between Bitcoin, and your network. Or if you could enable new features through commitments, and disable them just by moving coins on-chain, and not committing to those features again in your new transaction.
You can read some articles by Paul Sztorc to know more about it, for example:
https://www.truthcoin.info/blog/one-chain/As you can see, the title "One Chain to Rule Them All" means it is compatible with your question.
